If you have got as far as removing the screw cover. Squirt some WD40 on the screw, it is more than likely partially seized. The head of the tap needs to be wiggled from side to side, or struck lightly from below... strike one side then the other ...
Dont use too much pressure... but they all come off in the end.
I then usually grip the spout of the tap with a large pair of grips with soft jaws, and undo the rest with an adjustable wrench or spanner.
It went together so it must come apart ... If I get a difficult one, I use my 12" pipe grips to hold the spout of the tap. and large adjustable wrench to free it ... or as a last resort a stilson wrench. If I get this far I usually end up replacing the tap anyway.
A bit of heat from a blow torch will help ... but dont overdo it, or you may crack the basin.
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