NASN is part of Setanta now, you pay ?14.95 per month over and above whatever you pay for Sky or cable (our Sky bill is ?34/month plus NASN, but we have all the sports channels). Their adverts say they'll be broadcasting something like 250 MLB games this summer, and so far they seem to have 3 or 4 a week, including a Sunday evening double header. The Astros have been on twice, once against the Nats, and once against the 3rdinals. They broadcast live, but they also replay the games 'as live', meaning in full, the next day at more hospitable hours. Channel 5, a terrestrial station, also does one or two games a week. IIRC, they show the ESPN Sunday night game, and 1 on Wednesday (I think), but those are on at 1 or 2 am.
If you sign up for NASN, you'll also get Setanta Sports 1 and 2 and Setanta Ireland, plus the Rangers and Celtic channels. Setanta is great for watching Irish sports, like hurling and Gaelic football.
And Limey's right--everything is incredibly expensive in London, and you end up with pounds (no pun intended) of change; imagine instead of a $1 bill you had a $1 coin.
Happy to help with any questions on living here, from an American point of view! It's great here, you'll love it.