One option is to get an IPTV service and use it with an app where you can record the shows on disk (like TiVo I think you guys use, heard that a lot on older TV shows lol). Will only record future shows but tbh, a lot gets repeated on their other channels (www.channel4.com/tv-guide).
Using a VPN is another option but I recently couldnt load the app while using a lesser known VPN from within the UK so they seem hot on blocking them.
Another option is rent a cheap VPS from in the UK to act as your own VPN.
All of their shows is on their app, and they have a pretty cheap ad free option if you can figure that out too.