I did this last November. Worked perfectly. I booked a Monday 9am appointment and got there around 8:50.

I waited a while and was back outside with my new passport (and the corner snipped off the old one) around 9:20am. Liz line from there to Heathrow is also very convenient.

All in all, a very easy process. I think it would have been quicker if I had made a slightly later appointment as there was a bit of a crowd for the 9am slot, which is the first one.

EDIT: Since last November, two weeks after I got mine, the official websites have updated their text to say the new passport will be given 4 hours after your appointment. Ouch!