Cabinets are also usually attached to each other at the front stiles, usually near or under the hinges.

Thank you for that. Yes, there was a screw behind each hinge. With these removed, the cabinet is slightly loose at the end where I removed the screws, but I still can't see how to remove it from the wall. The free end of the cabinet (i.e the end that does not join onto another cabinet) still seems firmly fixed to the wall, but I can't see how. There are no obvious screw heads or similar.

Thanks for any further advice - Rowan

Are they Ikea cabinets? Ikea uses a rail and bracket system for wall cabs.

No, I'm pretty sure they are not Ikea. I don't know what make they are. They were installed by the builder of our house 25 years ago.

You've tried raising straight up?

Yes, I had tried this. I have discovered that part of the problem was that the cupboard was stuck to the wall with sealer down the free end. i have now released this, and the bottom of the cupboard can now be pulled away from the wall, but I still can't find out how to remove it from the wall. I have again tried lifting it vertically upwards, but it doesn't want to move in this direction.

Did you find an answer to this, I have exactly the same issue?