This is a difficult one to answer, in a straight forward way. Many things to taking into account.
Did the basin tap ever have good pressure?
Is there good cold water pressure in other parts of the flat?
What type of heating system do you have? Combination boiler, hot water cylinder running with a system only boiler.
Depending on answers to this questions will determine its a possible to repair or new pipes, or even a cold water mains pump is needed.
It would be a blocked pipe or filter to tap , either with jointing compound or something has been dragged into the pipework from the storage tank IF it was drained completely and no gate valve was available to isolate the tank .