Re: What would be required (technically)
The question is not whether you use a UK-based ISP or not.
It's do you trust the connection, and to what extent?
I trust my browser.
I trust my machine (that may be misguided, but I think I'm generally okay there).
I trust my local network connections.
I trust my router.
All good so far.
What they are saying is that I can't trust transit between my router and ANYWHERE ELSE ON THE NET. That seems... pretty normal to me. Plain DNS is unencrypted, sniffable, and anyone at my ISP or in the path to the DNS server of choice can sniff, modify and insert traffic.
As such, the solution is not "move abroad" in terms of your connection, but realise what you are trusting that you shouldn't. DNSSEC is better, you can't "fake" or modify a DNSSEC response.
But even better is to not give anyone - the ISP or anyone else - the opportunity to monitor your unencrypted traffic. That means end-to-end encryption (HTTPS over DNSSEC loookups, because TLS etc. does in fact TRUST the DNS response to be authoritative and correct!) or VPN to a trusted location.
If you buy a virtual server, pretty much the web filtering on those isn't present. They aren't classed as ISP's so they don't filter sites, play with DNS responses or limit access. They are much more concerned with billions of spam emails or you trying to spoof an IP. As such, the cheapest virtual servers, at home or abroad, can be hand for a few pounds a months and you can configure your router to VPN to them and route all traffic through them. Voila!
Or, as you suggest, you can just a VPN host that you trust and do the same.
But the problem really stems from so much stuff still being plaintext and unencrypted. Email. DNS. HTTP. Even DHCP (how do you know it was your ISP that gave you that IP address and that you weren't shifted to a different IP by some blackbox that your ISP was forced to install?). The solution is to move to DNSSEC, HTTPS - we don't have a solution for email yet because people apparently don't think that billions of unencrypted-by-default emails matter - and encrypted-by-default protocols everywhere. Also, VPN access.
My phone can do VPN access to my virtual server. I wouldn't join a hotel wireless network without it. And I can provably connect to ONLY my VPN server, with no middle-man, or not connect at all.