I'd be thinking about an unvented cylinder (runs at main pressure). Megaflo is one brand name.
To make it work properly you will need good water flow and pressure into the house, which usually means replacing the old service pipe to the pavement with a new, larger, plastic one, and continuing the larger pipe all the way to the cylinder and bathtaps. It's important that the pipes are not throttled with small valves or sections of small pipework. The large valves are relatively expensive so some plumbers will fit small ones. 32mm pref but 25mm will do.
Running the pipe out to the road will need a trench. Builders will do that. Plumbers are weedy fellows. It need not follow the same route as the old pipe. Ask your water co to test your drinking water for lead content as there might be a subsidy, or free reconnection. Ask now as there could be a long delay, and it must be completed before starting work.
You will need a good local plumber, by recommendation, who will be familiar with the job. He has to have a G3 qualification, not all heating engineers do.
It's possible to continue using the old boiler but this might be a good time to replace it. You need a heat-only, conventional or system boiler, not a combi. Opinions differ, but it may well be more reliable.