An unvented (pressurised) cylinder can give unsurpassed hot water. However since there is no cold tank you are dependent on the flow and pressure coming into your house from the main in the pavement.
Fill a bucket at your kitchen sink, time it, calculate how many litres per minute you get. Do the same at utility room tap and garden tap if you have one.
If flow and dynamic pressure are poor you would probably benefit from running a new, larger plastic supply pipe to the pavement, in 25mm or preferably 32mm blue plastic.
A large one is usual. A typical 250 litre cylinder weighs more than a quarter of a ton, so preferably put it on a concrete ground floor, and certainly not in the loft.
You can run it off any boiler, including your old one, or a combi, but get one with two electric immersion heaters, one at the top and one at the bottom, then you can have hot water when your boiler is out of action. Sadia and Santon are two good UK makers.
p.s.
I suggest you buy a new kitchen tap anyway. A UK tap, not a flashy stylish import. Bristan are very good.