Well that was fun while it lasted.
If you want ESPN America now, you have to subscribe to Sky Sports and add ESPN America on top of it. If you don't have either one at the moment, you can add both for £27/month, which, in my opinion, is a rip-off. If you already have Sky Sports, you can add ESPN America for £9/month, which is also, in my opinion, a rip-off. There doesn't seem to be an "ESPN America without Sky Sports" choice.
This year we're going to get a Sling Box, set it up at my parents' house in the states, and watch the NFL over the internet.