The problem is, of course, that the catch sits behind the chrome radiator grille and the linkage that opens it is all hidden under the bonnet. If the jam happens when the grille is in situ it is very hard to get "persuasive" with the catch or linkage components without damaging the delicate grille slats.
Bonnet catch problems generally happen for one of three reasons: 1) the release mechanism suffers a mechanical failure, 2) the bonnet is fully closed before its position has been properly adjusted after re-fitting or 3) a front-end impact causes bonnet distortion, putting inappropriate stress on the catch.
My most important point is in capital letters to convince you that I really mean it:
IF YOU HAVE REMOVED YOUR BONNET AND ARE REFITTING IT, DO NOT REFIT THE GRILLE UNTIL YOU ARE ABSOLUTELY CERTAIN THAT THE BONNET SITS CORRECTLY AND THE CATCH IS WORKING SMOOTHLY AND EASILY. TEST IT MANY TIMES.
If you pull on the bonnet release and nothing happens, it may not be as bad as you think. First, get an assistant to pull on the release while you give the bonnet a hefty upward tug. If it springs open, then you have been lucky this time but you need to adjust the catch urgently (see below).
If the bonnet stays obstinately shut in spite of your hefty tug, then that suggests that the release linkage is not working properly or the catch is jammed. You will probably have noticed that the bonnet catch consists of a stud, shaped a bit like an inverted mushroom, which fits into a hole and is held in position by a sliding lateral retainer. The mushroom stalk has a spring that is compressed on closure and pops the bonnet up as soon as the retainer is withdrawn sideways by the release mechanism. If the stud will not withdraw from the hole, then either the retainer is not moving or the stud is badly jammed against the side or bottom of the catch.
STEP 1: check visibly whether the retainer is sliding sideways when the release is pulled. If it is moving, go to STEP 3. If it is not moving, go to STEP 2. During this visual examination you may be able to see, also, if the stud appears to be caught.
STEP 2: You will need to actuate the release by inserting a suitable tool between the grille slats to drive the release mechanism to the right. The mechanism runs under the catch panel, so you need to get down low and look up at it to see what is required. You may need to use impact or leverage, or even a combinatin of the two. e.g. poke a bar through the grille and rest it on the end of the release lever then whack it. Or use a longer bar and use leverage, with your knee as the fulcrum. When you get it right, the catch should pop up and you can open the bonnet to find the point where the release mechanism has failed. It has a number of joints and pivots where this could happen. I know "a suitable tool" is vague and it is intentionally so, because this is one of those cases where you just rummage around the workshop until you find what you need. It may be an old screwdriver or chisel that you can bend a bit to fit. Or just a bit of steel bar. (In the interests of your personal safety, do not be tempted to rummage in the kitchen drawers).You can wrap the tool with rag where it passes between the slats but I fear you may find that a bit of slat bending is inevitable. As long as the metal is not stretched, you will be able to take the slat off later and get it back to its original shape. The hard bit is getting enough force applied in the right direction without using more force than you can control to prevent damage.
STEP 3: If the retainer is moving clear of the stud, but the spring is unable to pop the bonnet up, it is likely that the stud is out of alignment either because of maladjustment or physical damage and the flat edge on the stud head is catching on part of the catch housing. This is where I shamelessly reproduce the advice that Trevor gave Sylvester:
"The bonnet should have some flex in it. Ease the bonnet down a little and try to twist the front to release or reduce the stepped head's grip on the raised plate, then lift/jerk the bonnet upwards quite hard. it may help to remove the security latch if possible. A second person can help either by applying pressure on the offending pin or just adding muscle power. The front valance can be removed (I think) from under the car, this bolts on to the front wings, and the front chassis member under the radiator this also means the front bumper , fog lights wiring as well coming off, a lot of work, but it will give you a bit more room and possibly save the grille.
The only other option is to knock the pins in the bonnet hinges out with a small pin punch. They will go out easier one way than the other, if you go this route make sure you use plenty of sticky tape before you start on the wings, bonnet scuttle etc to ensure there is no paint damage. This IS a two man job to ensure minimum damage.
If the bonnet is too far forward, the pin therefore needs to go back towards the rear of the car. If the pin deflected enough on the down stroke it will deflect enough on the upstroke,. Get a piece of 5 to 6 mm flat metal bar ,say 25mm wide, onto the pin through the grille bars, (a bit of tape around the steel bar as it passes through the grille) With the help of an assistant ask him or her to lift the bonnet until it stops, keep pressure on the bonnet and with the bar on the pin hit the end of the bar with a good size hammer. You may need to to this several times but the pin should spring past the raised metal plate. Do not hit the pin too hard or it will bend backwards, just enough to spring it.
The biggest problem is that the assistant is in the way. Get them to stand on two chairs one either side of the grille with their legs apart ( you will find out who your friends are, that is for sure! Swinging a large hammer between someone's legs calls for faith on somebody's part). The pin should spring back enough to jump the plate with the upward pressure.
One tip is cut a 45deg vee in the end of the bar so that it sits on the pin and will not slip off the pin as you hit it."
Before you attempt to adjust the catch, check carefully for any distortion in the underlying bodywork or the catch components themselves. If your catch stud is worn or you trash it during your rescue operation, don't worry. It is a part shared with the MGA and is readily available new from the usual sources.
FITTING AND ADJUSTING THE BONNET
First fit the bonnet without the stud part of the catch. Get the gaps and the alignment right using the adjustment on the hinges before you worry about the catch adjustment. Once you are happy with the panel fit, re-fit the catch. If the bonnet has not been repainted, there may be some old marks to guide you but if not, start in the centre of the adjustment range. Then, lower the bonnet gently towards the catch and assess the position of the stud in relation to its target hole. Once you are happy with the position of the stud, you need to adjust its length. This is done by releasing the lock-nut and screwing the stud in or out until the length is right. If it is too short, it will not fully engage and the bonnet will pop back up. If it is too long, it will engage but the bonnet will not sit tight on its buffers and will probably rattle. Start long and adjust it up until it clicks easily shut with downward pressure but is also firm on its buffers. During this process, you need to nip the lock-nut up enough to hold the position while you test it. Tighten it fully when you have achieved the right position.
Now check the release (having greased all the moving parts). You should not have to pull too hard on the loop under the dash to make the catch open and the bonnet should clearly pop up. If it does not ,and you need to pull it up, it needs more adjustment. Keep at it until you get it spot on: you'll never regret it.
Thus far I haven't referred to the safety catch because it rarely causes problems. It is designed, of course, to stop the bonnet opening fully after the main catch has been operated, in case a malfunction of the catch releases the bonnet on the road. The air pressure underneath the bonnet will lift it in spite of its weight, with disasterous consequences when it flies back against the windscreen. (Don't ask me how I know - I'm still having the nightmares). Once you have adjusted the main catch, make sure the safety catch is engaging properly and can be released easily before the bonnet is fully lifted.
Fletcher Millmore, in the States, who is undoubtedly a sage when it comes to matters MG, also added a comment to the thread:
"I've never met a bent latch pin; they are hard as he!!. And I have corrected distortion of the mounting panel with a piece of pipe on the pin (i.e. for leverage). The usual problem is that they are adjusted down too far and snap under the bottom piece. This should have a lip on it to prevent the problem, if assembled correctly and not too far out of adjustment (1/4"+). The bonnet should rest on its support buffers before the pin goes that far. I always check that the pin is central in the latch hole before letting it down, a matter of parts alignment - fore and aft being the more critical direction of concern. If so then press down until it latches, at which point the bonnet should be in light contact with the buffers. You are then able to press the bonnet down a bit more against the buffers, but not enough to cause this trouble."