You could spin up a DigitalOcean droplet in the London region around once a week and use youtube-dl to download the bits you're interested in. Cost would be like $0.10 per month. You could even make a script that sets up an OpenVPN droplet and automatically tears it down, would still be very very cheap.
If you set it up manually each time, sure, that won't work very well. But you should be able to automate that - create the config (CA and everything) once and then just spin up a droplet via the API, install the packages, copy and unpack the config. I don't think you'd need to customize more than the sever's IP address in the config.
I built something similar with sshuttle (way easier than OpenVPN) two years ago, it's at https://github.com/lorenzhs/instavpn but it uses the old DO API and is rather hacky. sshuttle also isn't very good for streaming.
