Turn cold supply off will it will stop hot after a small amount has run off,no need for a hot isolation valve.
On another note it’s a very poor installation that is not to standard.
Without seeing your system the gas boiler can operate the hot water heating via the cylinder and the radiators ,both can be set independently ,the gas boiler will operate when the clocks and thermostats are on.
Probably pre 1990 ,will have a separate hot water heater either attached seperate, some people love them ,not very efficient and as far as replacing it’s compete system .