I eventually managed to figure out the solution to my internal server error problem: it was simply that there wasn't enough free webspace left on my 123-reg server. (I would advise all WordPress users to check this out with their hosts as a basic first step when internal server errors appear - i.e. before they make any unnecessary changes to their files/settings/database etc).
That only came to light after trying all of the aforementioned steps (and replacing my wp-admin and wp-includes folders with the latest WordPress versions - which might actually work for your specific problem, because it sounds like some of your files might have been corrupted). I also deleted some test sites and their corresponding tables from the database, thinking that the database space might have been exceeded.
Here's my response to 123-reg:
"I appear to have found the solution to my problem - no thanks to the 123-reg support team, who were absolutely useless.
It seems that my webspace quota had been exceeded. I deleted some files and can now post new web pages etc.
I've complained about this before - there is no easy way of monitoring web space usage from the 123-reg control panel.
I would have thought that one of the first checks that 123-reg support would have carried out when I first raised this issue would have been to check web space/database usage.
If this is the level of support to be expected of 123-reg, I think I'll be moving all of my websites and domains to another provider."