Its very unlikely that you have a blocked pipe ,not impossible ,but highly unlikely. Did original tap ever work properly ? First thing is to focus on the iso valve that you have in vanity unit and go from there.
Ok, we moved in and the tap didn't work correctly. Hopefully its the valve.
Could it be that your tap is not suitable for low pressure systems? I've definitely seen that before where cold is mains pressure so works fine - well I've seen it on showers and pretty sure same would apply
It's a combi boiler. Is that a low pressure system?
If it was to be the valve, I simply turn off the boiler, to stop the flow of hot water and replace, right?