My cousin was not in London during the bombings, and she and her family are fine. She wrote this to Mom today about the trains:
Our train line runs directly to Kings Cross. I was going to meet my Belgian friend next Tuesday but he has begged off coming over.
Our trains are still stopping at Peterborough and then buses take passengers into London [and ditto for the return]. GNER is the premier line in Britain going London to Edinburgh and as far north in Scotland as Inverness, so you can still get around and to interchange points to get to other places. However, the Underground Line [Piccadilly] which was bombed runs under the main line train station so they are keeping heavy trains out while they check to see how much damage there is to the tunnel. They estimate it will be three weeks before the Underground will be back to normal, and so most people who are not working in London or need to go there, are just giving them time to sort things out.