Firstly from the description you have given it is the actual intenal part that is leaking and there is no need to remove the tap from it's mounting.
Take a very small screwdriver and remove the small bubble under the handle (at the front). It will just pop off.
Behind this you will find a 2.5mm 'allan key screw'. remove carefully with an allan key.
Lift off the tap head - you may need to wiggle it a bit.
Underneath you now have access to the tap internals. Using a pair of grips remove the top nut and this will allow you to take out the tap cartridge.
Replace with similar - either Reich or equal. You will find that if you disamntle the old cartridge the washers inside have been damaged or the ceramic plate is cracked. This is most likely caused by frost damage during the winter lay up. Taps should be left in the 'OPEN' position during the winter lay up.
The cartridge will cost around £11 up to £16 depending upon where you buy it, They are available on line.
REMEMBER - the cartrdige has 2 locating points on the bottom. Make sure you drop it back into the locating points otherwise you will over tighten it and will have to buy another one.
Rowantree - Autosleeper Fan, May 2009