MakeMeStronger
it sounds like you have an old system with a gravity feed to the cylinder. This also takes a long time to heat the cylinder. The cylinder is probably a copper coloured one.
This can be altered at modest expense, you don't need a new boiler, but you do need a thermostat on the side of the cylinder controlling a 2-port motorised valve on the pipe that goes from the boiler to the cylinder. It may be a 28mm pipe and the valve will be more expensive than a 22mm pipe.
if the boiler and cylinder are fairly close, it is not much of a job, but if they are a long way apart, a cable has to be run between the two which might mean taking the floor up.
A better, but a bit more expensive, way would be to convert it to fully pumped, with a three port valve. You will still need the same thermostat and cable.
Better still would be to do all that and also fit a new cylinder, which will have a faster heating coil and factory-applied insulation.
None of these jobs involve work on the boiler, so you do not need a gas-safe engineer, but an experienced plumber or heating engineer will understand the procedure.
In the meantime, it is very important that your cylinder, and the pipes between it and the boiler, are very well insulated, as they will be wasting energy during warm weather. Use two red jackets, and climaflex or similar on the pipes.