Water tank not heating?

For the past week I've had no hot water - there is water coming out of the hot tap, but it is cold. My boiler fires up as normal, and the heating works, but no hot water.
The pipes that run up from the boiler to the hot water tank are hot, as are those that I think feed into the tank (these are at the bottom of the cylinder).
The cylinder itself doesn't heat up.
Occasionally I will get about 2 minutes worth of hot water, and then it just goes back to cold.

Please help - I'm bored of going to the gym just to have a shower!

Thanks
Mhairi