Hot water only lasting for around 30 seconds

Hi

When we turn on the tap, the water comes out cold, then hot for around 20-30 seconds, then goes cold again and doesn't get hot no matter how long we leave the tap running. The fault light isn't flashing, an electrician has looked at the boiler and thinks that the problem may be the pump, also the relay is making a rattling sound.

Does anyone have any idea how this may be fixed? Gledhill want £300 for repair, is this a good price for the repair required? We live in the Dudley area.

Thanks

Included in the £ 300 is there break down cover for a year?
If so may be a good deal if you have no one local.
There are many things it could be.
And some are expensive.
Mike