After the engine transplant and the oil warning light coming back on, it turns out that the pump wasa broken. It's been replaced and is now working fine. The screeching sound from the belt was also reported to the mechanic so he fitted a new one.
However, half of the time, I'm still getting a screeching sound from the new belt. Why is that? Usually in lower gear, though not always, but sometimes in higher gear. Other times the car runs fine with no noise from the belt. What's with it?

Check that the belt tension is correctly adjusted. If it is, then something driven by the belt or a tensioner pulley is imposing too great a load and the friction is causing belt slppage.

Thanks for that. Can I just add that it only happens occasionally. But when it does happen, often when I'm stopped in traffic and rev a little while holding down the clutch, the screeching fades away completely. Although again not all the time, but enough times not to be a coincidence. Does this suggest anything in relation to the clutch?

The clutch throwout bearing can make noise, usually a rumbling or clicking sound when the clutch is depressed, but squealing is certainly possible.

So it might not be the belt??? It does sound like a belt, but as I've said the mechanic fitted a new belt! If it's the clutch, what should I do to sort it out?