I guess it will all depend on the type of system I have and the main
question will be whether I have to connect the two radiator pipes
together to allow the water to flow, or if I can just run the system
safely with the gap in it.

Should be fine. Almost all UK systems are twin pipe and don't require the
ends to be linked. Ancient systems (unlikely as you are combi) or US systems
may require linking.

It is important that you don't rely on a TRV as an isolation valve, as they
don't normally turn off fully, but go to frost protection mode, where they
can open if it gets cold overnight, emptying your system over the carpet. To
turn them off completely, you normally need a decorator's cap which holds
them fully off. (My TRVs actually have a genuine off setting half a turn
beyond the normal frost setting).

Christian.