Thank you very much Pat ! It was a bit hair-raising. I wanted to be sure it was an easy transition so phoned the Server. The man I spoke to was adamant. No, I would not have to make any changes, yes Google would update it, yes everything would be easy. . .
Why did I believe him ? First thing were all kinds of 'DANGER !' messages and emails from people who could not get to the site from Google. I managed to get to it in the end, but nothing worked - so I thought carefully and realised I needed to change links in all the scripts which run the program. There are dozens of them. Then I chickened out, didn't dare upload the new scripts so I called my computer guru who came over a couple of hours later, checked my work (and found a load more to do. . . ) and we opened a couple of cans of beer, held our breath and uploaded the scripts.
Phew ! It all worked fine, but now how to get the change publicised - I don't do FaceBook. Luckily lots of helpful people are putting the new address about, and hopefully Google will find it soon.