I wouldn't give up without doing a bit more reading up OP. A mid-terrace is naturally quite an efficient shaped building (two walls 100% insulated by the neighbours!) though of coures it also depends on what your windows and roof are like. But I expect you have done the basics of insulating the loft to 300 or 400mm etc.
We are planning to get a heat pump as the gas boiler is on its last legs, and so we did a 'trial'. (We basically turned the boiler down to run the radiators at about 40 or so degrees (which is what a heat pump does) and let it run to see if we were still warm - and we were. (we did this in winter obviously!!) If you have enough radiators then 40 or 45 degrees will heat your house, you just need to run the heating for more hours to make up for the lower temperature. You are putting in exactly the same amount of heat, just more slowly. And using less energy to make the same heat because heat pumps are so efficient.
You can also get more heat into the house by swapping some radiators in the biggest spaces for extra-big radiators (even triple ones) - these are not hugely expensive. Or adding one or two small ones eg in a hallway or landing. Underfloor heating is ideal, and wonderful to have, but obviously that could end up costing more than the heat pump!
But basically you need someopne who knows what they are doing to come and do some calculations. They will work out what size heat pump you need (the more efficiency improvements you've been able to do, the smaller the heat pump can be) and how much radiator area you need to get the heat into your house (you might have enough, with 13, but an expert will measure them for you and work out if they are right for your rooms) and also if your hot water tank is in a suitable location and well-enough insulated. (you might need to get a new, bigger coil, on the same basis that you might need bigger radiators)
They should also tell you what subsidy you can claim. There is a good pay-back on heat pumps at the moment, but in March it swaps over to a cash-up-front arrangement, which might not be quite so generous, though it is is still pretty good
Definitely google and read around on this. And if you decide to go for it, be fussy about your installer, as some of the bad experiences come from bad installations (pump too small or too big, radiators or timers set up wrong., etc) , rather than heat pumps being inherently unsuitable.