It's years since I had to go to central London regularly, but I found that the best way was to cut across to Wembley Park, which is two stops on the Metropolitan Line to Baker Street, which, in turn, is reasonable walking distance to the PO tower. Of course this was before the M40 and I was coming from the M1.
However, it may well be possible to park at Uxbridge, just off the M40 and do the same.