As the rugby was on today I have *once again* been digging around for a fix to this. It seems I might just have one; and it's unexpectedly simple - or so it seems.
1) I'm connected to my VPN, with my ip address in London.
2) I open my browser and go to http://www.tvguide.co.uk/ [free/no subscription/apparently no ads either]
3) and there are all the UK TV channels. Or all the main ones plus about 50 in total.
4) I just watched a test-period of live tennis on BBC1 - no probs. I then watched some F1 racing on C4, which is now followed by live horse-racing.
Hmmm.... seems almost too simple to be true, but we'll see. Note: I'm not in any way connected with the linked company, it just came up via some intensive Googling

ps. Another suggestion that came up in my research was accessing via a VPN and Hola [Hola.org]. I haven't explored that further yet and won't as long as the previously linked keeps on working.
p.s/ADD: Live Euro 2016 [football] on ITV works too....