According to Phone arena, that phone supports the following bands
850, 900, 1800, 1900 MHz
850, 1900, 2100 MHz
HSPA (unspecified), UMTS, EDGE
Those are pretty much the same frequency bands supported by my Nexus One, which worked just fine in London last year. The sim will determine the network the phone connects to, so since the H2O sim already works, I see no reason why it wouldn't in the UK.
I was told that not only won't it work in London, the phone will not even activate once the H2O SIM card is put in. They said the phone is locked to AT&T and will display "Inoperable" if any other SIM card is installed.
Once you go overseas, the phone itself - regardless of what SIM card is in it - won't connect to the network and therefore will not work outside of the US.
AT&T and Best Buy really need to work on their training.