Put a 308 in it. That usually fixes that problem.

My guess is timing.

Is it an auto or manual? Could be fuel restriction as John hints or even a failing fuel pump or similar. Is it a late HQ with canister?

It may be the condenser in the dizzy failing under load too.

Richard, I wondered if it was the attitude of the car, rather than the engine load causing the problem.
I'll resist the temptation to to flippantly advise that you have insufficent cubic inches, since that has already been done.

Some of the best possibilities have been covered by John, Byron and others, but I'll elaborate on a few.

The fuel pump uses vacuum to draw fuel from the tank, so a dodgy fuel pump check valve, and/or leaks in the pipes from the tank to the pump would cause the pump to struggle, particularly when it has to draw fuel to a greater height such as when the car is on a "really steep hill".
If you have access to the equipment a pressure test of the pump output with the engine at idle should show between 3 and 5 p.s.i.

If fitted, the screen on the fuel pickup (in the tank)could also be partially blocked, and you could also have water in the fuel tank which only gets drawn into the pickup when the front of the car is elevated. If you have the clear sight glass on the pump you may see some evidence of this.

Plug leads are a likely cause too. You can test them with an ohm meter. You should see between 4000 and 8000 ohms per foot. (Assuming they are carbon string type leads). Don't forget the one from coil to the distributor cap.

The condensor is a possibility too. In a Kettering ignition system it extends the duration of the spark after the points open, and if it is weak or low in value, or improperly connected, you will have a short duration spark and less ability to ignite rich fuel/air mixtures. Check that the earth screw securing it to the distributor is tight, and that the connection is clean, and do the same at the points end. Or just replace it.
For a similar reason it would be worth checking the point gap.

Is the car actually in the UK? If so, I assume that may make getting bits and pieces difficult.
Good luck.

gm5735- Thanks for all those tips. I'm going through them one by one
Yes the car is in the UK, but I have a good stock of most things including spare fuel pump, dizzy, carb kit and basic stuff like points and condenser I can get over here. I changed the plug leads today, but no influence on the problem .Plugs, points and condenser are virtually new and all contacts are good.
I did manage to get it to falter on a flat surface today so it looks like it is more to do with outright load level than the result of being on a steep incline. Kickdown also seems to work fine.
As much as I like the 308 idea, I don't have one of those over here, so I'm going to have to chase down the problem with the 202!
Just to put something else into the mix, I use Castrol Valvemaster lead replacement in every second tank of fuel I buy. A friend over here with a MK3 Cortina won't use it as he reckons over time it leaves sticky residues in the carb that ultimately give you the kind of problem I've got now. I'm not sure if this is true or just a myth, but the plan is to give the carby a good clean and see if that helps. I'll let you guys know if that solves it, but thanks to everyone for giving me a list of possibilities.

Is the dizzy mechanical advance working ? stuck or broken spring ? and just advancing on the vacuum advance side.
Put a timing light on it with the vacuum dis connected and see what she does.