Hi Spitty,
Bad news I'm afraid, you will need to go back to London for another visit to the US Embassy.
I have just returned to Florida for more flight training having previously been on an M-1. Like you my interpretation of the Embassy's website was that I didn't have to go for another appointment. I emailed and called to verify this but was informed that a trip up to London was once again necessary.
It is also going to cost you more this time as well I'm sorry to say. You will now have to pay a $100 fee to SEVIS, who the flight school will use to issue you your I-20 form, I know of at least one person who already whose visa has been declined as they did not take the receipt of payment for this with them to the US Embassy.
Also you need to pay a fee to the TSA, which I think is $130, this started on Wednesday this week. Check out this thread started by NAC if you haven't already.
TSA Training Rule
Sorry to be the bearer of news of more expense!
With all the fees be imposed on foreign students wishing to train in the US now, I think there will come a point soon where the hassle of all the additional paperwork and new fees being introduced will not justify the constantly reducing savings over training in Europe.
Good luck with it all.
Matt