A good undercoat is key to achieving a good finish on painted woodwork like this. A tin of Crown brilliant white or white undercoat will do the job, however to cover darker colours an undercoat with high opacity i.e high colour density, will hopefully negate the need to apply more than one coat...
I currently have a tap like this one: http://www.sinks-taps.com/item-3745-HILTON_Single_Lever_Kitchen_Tap.aspx
I want to replace with one like this: http://www.sinks-taps.com/item-3887-RENO_Single_Lever_Tower_Tap.aspx
which is described as a high pressure tap. The cold is mains pressure...