Thanks for the suggestions.
My discs are Verbatim AZO.
I tried burning a disc image with Apple Disc Utility and received messages saying "burning to disc" and "finishing burning" within seconds of each other, whereupon the disc popped out. There was nothing on it.
I finally tried iDVD because I had actually used it a few days earlier to make a DVD but was disappointed when the picture kept freezing at irregular intervals. It was then that I decided to buy Toast because i thought it would have a higher spec.
When however, both Toast and the Apple utility failed, I had another go with iDVD and actually got a readable DVD. Hoping that perhaps any problem might have resolved itself, I had another go with Toast. The encoding and multiplexing went well, the writing to disc went well until it came to writing the lead out. At that point the following message popped up:
The drive reported an error:
Sense key = HARDWARE ERROR
Sense code = 0x44, 0x86
INTERNAL TARGET FAILURE
The disc was apparently readable by my Sony DVD player. It showed me the menu, allowed me to select the first option (but not the second - that just lead to grinding noises) but the recording stopped well before the end so the disc is useless.
I did manage to copy some photos on to DVD via Toast as a test. That worked but the Hardware Utility now refuses to recognise any disc. It just puts up a "waiting for the drive message". As it won't recognise that it has disc in it, you can't ask it to eject the disc, let alone burn it.
I have contacted Apple support and am waiting for their reply. I shall also buy another make of DVD disc as a test.