ugh... we need to make a distinction between good science and bad movies, specifically when talking about bad science in bad movies.
for answers here, i refer to the ubergeeks at badastronomy.com where I sometimes also contribute. not surprisingly, there was a thread about this about a year ago.
http://www.bautforum.com/showthread.php?t=13142
essentially, what it said was that the ten or fifteen miles inland from the coast would be affected. which is bad, but not civilization-ending. There are a few things contributing to that. One, the easter seaboard in most places tends to gain elevation fairly quickly. Two, there's an entire mountain range (the appalachian-allegheny range) between the wave and the ohio valley.
on the minus side, the 2005 tsunami was felt clear up to alaska. (water rose by about a foot or so there). So we're looking at everyone in the atlantic - north, south being affected. England wouldn't even be a speed bump. The straits of gibralter would probably buffet the Med, but expect a wave of that size to go around the horn of Africa and do some damage in the indian ocean (especially in those low lying islands). I'm not going to try to figure out the damage or the deaths - i figure with two years notice that enough people will have moved out of harm's way.
Oh, and blowing it up is probably the worst thing you can do. Unless of course you like volkswagon sized shrapnel hitting the atmosphere at extreme velocity.
as for the origianl asteroid (i.e. the 1 mile one) according to a risk assessment for the NASA Cassini probe launch (don't ask why.. it's just there for comparison's sake because some nit wits whined that the probe would kill us all if it fell back into the atmosphere) for a 1 mile asteroid strike you're looking at 1 billion dead. For a 6 mile asteroid (i.e. roughly on par with one that killed the dinos) you're looking at 5 billion dead. And for an asteroid about 1000' wide, you're looking at 5,000 dead.
http://www.dartmouth.edu/~chance/course/Syllabi/97Dartmouth/day-6/risk.html
so yeah, somewhere between the 1 and 6 mile range you get a rock big enough to ignite the atmosphere (which is what happened at the end of the cretaceous - global firestorm and all that. for the 1 billion, you probably have localized (half a continent) damage plus the associated secondary deaths.
Oh.. and here's a link to a study stating that asteroids smaller than 1km are unlikely to cause tsunamis.
http://www.bautforum.com/showthread.php?t=4035
John