Yes, it very common for people to fix the problem, but not the cause

, from what you say it sounds like the issue has been coming on for a while. Is it possible you had a slow water leak or it needing coolant topping up often? When heater stops working but all else seems good that can be an early warning that there is air in the heater matrix/radiator and if allowed to continue the lose of coolant water around the cylinder is next. After that failure is imminent.
Even if you have a slow leak , as long as it is kept topped up then not much damage occurs as water cooling works, once the water level drops and what water there becomes gas/steam it can quickly reach way above the boiling point of water 100 degrees C and becomes super heated steam, so the head warps and the gasket blows etc.
The dying on start up could have been the early stages of the head gasket failure letting water get to spark plug causing a small misfire which soon clears with a quick rev up.
In fairness belting along the M4 by the time you were able to stop a fair bit of damage can have occurred, so if you do decide to do the work , once the head is off before anything else I would have a good look at the cylinder bores for any scoring etc. and then turn engine so all four pistons are at the same height and put an equal amount of oil on top of each piston, if it disappears fairly quickly or not at an even rate across all four cylinders you may have caused major engine damage beyond a head gasket job. Assuming that test is all good then it is wise to clean the surface of the cylinder block and check that for flatness using a steel straight edge and a feeler gauge, only after that start spending on head work and gaskets etc.
Sorry if I am going into too much detail, but I have seen people spend money doing the head gasket only to find the engine underneath it is knackered.