Our pump failed a few weeks ago, I removed the top of the water tank, turned the tap on, got hold of the pump and gave it an almighty thwack on the side of the tank whereupon it started working again!
Before you do this though, check you have 12v at the connector to the pump above the water tank (it's the one that goes straight into the tank, the one in the lid is the level sensor.) If you have 12v here then the problem is the pump. You might be able to fix with the method described above, or if not then there are plenty of replacements on eBay for £15 - 20 (it doesn't have to be the same make - try Whale). If you need to replace the pump then cut the connector off the old one and attach it to the new one with a chocolate block connector, after first passing it through the small hole in the tank
If you haven't got 12v at the pump connector (and assuming you've checked the fuse) then remove the kitchen drawer and feel up at the back for the wires to the tap. There is a connector here so check that 12v is going to the tap. If 12v is present, then the microswitch is faulty; I understand that this can be replaced very cheaply without removing the tap, there is a thread about it on here somewhere - Hotel California will find it for you if necessary!
The top of the water tank can be difficult to remove, I made a tool out of a piece of wood, drill two holes just smaller than the diameter of the top and insert two nuts and bolts to slot into the vanes on the top to unscrew it.
Good luck and keep the cash in your pocket.