Until this morning, Opera was running fine on my 32 bit XP machine.

Did an OS reinstall to get rid of a niggling problem. The niggling problem has gone, but so too has Opera.

Now find it will not reinstall: some kind of incompatibility message flashes when installer should run, but lasts about a tenth of a second, so I cannot read what it says.

Boo hoo! is there a fix?
Opera Software announced yesterday that Opera 36 will be the last version of the web browser for Windows XP and Windows Vista, and that all future versions of Opera would only run on newer versions of Windows starting with Windows 7.

The reason why support is being dropped in Opera 37 is Google's announcement back in 2015 that it would end support for Windows XP and Windows Vista starting April 2016.

Opera Software, unlike Google, plans to maintain Opera 36, the last compatible version for systems running Windows XP or Vista, so that users who are running XP or Vista can continue using the web browser.

above from here

I would advise you to download an older version of opera
Despite the fact Opera said they would support XP until at least 2017, they ended support last month or so early. Opera now only supports Vista and up. I myself was pretty angry about this since Chrome doesn't work and I HATE firefox since its slow to start and is kind of cluttery.
Thanks to all of you for all that information: have been too busy to keep abreast of the news in respect of this, and I had not realised that they had moved on.

Opera 36 now restored to said machine. Thanks.
I sometimes use Tor, yes, not often though because of reCAPTCHA deliberately breaking if you try to complete it on Tor Browser.