Steven P

Since the hot water supply to your bath tap is satifactory there is nothing wrong with your system, up to there.

The problem is downstream and is almost certainly a restriction of some sort.

I think it is unlikely that the pipe is significantly furred up. More likely is that the taps on your kitchen and bathroom sinks are not opening fully because there is some furring on them. It is also possible that isolating valves have been fitted close to these taps , to facillitate servicing, and that these are not completely open.

Do not start spending a lot of money until you are satisfied that the problem is not cured by simply looking at the pipes and stripping and cleaning the internals of the taps that are giving you the problem.

Regards

jcp