Thanks for all the advice, and yes, I did realise after I'd posted that running my own VPN was daft!
After a fair bit of research, I concluded that Nord VPN was best suited to my needs, and also was on special offer, so was only $3 a month for a two year package. It's not perfect, but seems to tick most of the boxes for me, the main ones being that I'm now using OpenVPN through it and that it has a reputation for not keeping logs. Being based in Panama keeps it out of the hands of the main government players, too (and my concern is primarily just personal privacy and the soon to come into force "snoopers charter" law here in the UK). Nothing I do online would be of interest to the intelligence services, here or elsewhere, so frankly I don't think they'd waste their time doing any detailed scrutiny. I just don't trust large, supposedly secure, databases that are ordained by governments, so having records hacked and misused is probably of as much concern as government agencies realistically taking an interest.
Thanks for all the help and advice, from a few hours of working with Nord VPN I can say there don't seem to be any obvious issues. Getting things working under Linux was easy enough, but required a session with the command line. Getting it working under Windows was a lot easier, everything ran from a simple GUI installer.
Speed seems unaffected as far as I can tell, and right now I'm sticking with a UK server, simply because its easier and my main concern is just keeping the local machine connections and data reasonably secure. Interestingly, it seems my VPN IP geolocates to around 300 miles away from me, as as far as I can tell there's nothing tracing back to my actual IP and location.
I'll give an update in a few days if there are any significant issues, but right now I think $3 a month is a pretty reasonable price to pay for a bit of peace of mind regarding our own government's snooping programme.