My hot water tap in the kitchen runs as soon as you turn it on, but as soon as it starts to get warm to hot, it stops running and just get the odd drop. What can this be?

What stops running? Does the on demand heater shut down ? Or do you think it's in the faucet? Let's check and see.
Shut off the supply to the heater and the cold water supply ton the faucet. Open up the faucet and remove the cartridge. Check the inlet ports for any trash. Place a pan over the open valve and turn on the heater supply. If the heater still shuts down the problem's in the heater. If it keeps running hot you have a blockage in the cartridge. Let me know what you find and we'll go from there. Good luck Tom

Hi there, many thanks for your input. I was a little confused, so braved it and took the tap to pieces. Turns out there was a washer missing off the inside bit of the tap (not sure what it is called... ), although it was looking very old compared to the cold water tap one (I took it all to pieces to compare). So I just bought a new internal bit for 4.49, and it works great now... no pricey plumbers bills after all... it is quite surprising what you can do if you only dare try :O)

Kudos and congratulations for solving your problem. (And a girl plumber to boot) You can go to work on one of my crews any time you show up. Good job Sally!
Cheers, Tom