Well thank you, everyone, for having taken the time to
consider and advise. Several of you have suggested the obvious - to ditch the old thing and get a new cheap one that goes fast and has lots of space and the January sales approach. Unfortunately, as I explained at the start, sentimental circumstances don't permit that yet. It's not the cash, I'm pleased to be able to say, it's that it was a gift from SWMBO's Dad.
Quite a few suggestions relate to ways of speeding it up, while staying with Vista. The thing is that it works fast enough after its weekly clean even if it only reaches the following Wednesday in staggering condition. My problem is the time it takes to do the weekly clean which fills the afternoon and evening, even when I don't do a backup to external HDD.
Perhaps there's a quicker defrag utility that Defraggler (because that's the step which really does appear to make the difference to performance) but I'm afraid Auslogics defragmenter isn't that solution. It's just as slow on this machine and doesn't recover the free space lost during the week. I'm sure that there has to be a faster backup utility than the Windows one which comes with Vista because it's desperately slow but it would have to be easy and I don't know which it might be. To compare, the Windows utility takes less than half an hour to defrag my desktop in W7 Ult.
Once it has been retired, I plan to clean it up and install Lubuntu or similar just for fun and to keep the brain cells stirred - I'll look at Mint too, now....
I probably explained myself poorly at the start of the original post. At the moment my problem is with the slow speed of the weekly clean up rather than with the speed of the machine after it has been done.