The two hours depends on how long it takes your bank to send money to our bank in London.
Sending funds from Europe will usually take 2 - 4 hours if your bank is instructed on a weekday morning.
US East coast banks can usually get money to us within 2 - 3 hours if they are instructed early in the morning. From later in the day on the East coast, or from the West coast, your money will usually arrive at our bank the following business day.