You're getting vapour lock in the fuel pipe. Petrol can't get to yer engine, engine dies through lack of fuel. It actually is
running out of petrol.
Quite common in hot weather. Happens to me Land Rover all the time, because the engine was designed to run on leaded petrol which combusts at a lower temperature. Today's unleaded petrol burns hotter, and while modern engines should
be able to cope, hot petrol + hot day + hot driving can be a killer combination for any engine.
In my case I can pump the hand lever on the petrol pump and force fuel through the vapour bubble, but I dare say your car is too new-fangled to have useful features like hand levers on the fuel pump.
The immediate fix is to stop - in the shade if possible - lift bonnet, let engine cool. It's the general under-bonnet temperature that's the problem, not the temperature of the actual engine, so don't worry too much about your temp guage or the radiator. You can usually start the engine again after a short wait.
If it won't start, remove the petrol pipe from some convenient junction point (I would suggest the carb, but I dare say your car is too new-fangled to have such a thing) and temporarily fix it where petrol won't splurge over anything vital. Spin the engine on the starter. This should push petrol up the pipe and force the vapour bubble out of the loose end. Re-fit the pipe and you'll be good to go.
But! As the under-bonnet temperature rises again the vapour lock may well return. That's why you can only go 300 yards before another conk-out.
The only real solution is to reduce the temperature of the engine bay. On my Land Rover I can do this by taking out the split pin on the bonnet hinge and lifting off the bonnet, but I dare say your car is too new-fangled to be so easily dismantled. Try fixing the bonnet in a slightly-open position, so you get some air flow through the engine bay.
It might be worth looking at the petrol pump - make sure it's shoving the petrol up the pipe with enough force. That won't necessarily avoid vapour lock, but it makes it less likely. Some guff about fuel pumps is here
. If there's a hi-performance pump available (possibly from the MG versions of your car?) it might be an idea to fit one. Don't think it's yer injectors, because this is only a hot weather problem.
Alternatively, fit a set of these
Otherwise, sell yer car to me for 20 quid.