The Publican will see to it that you do not take your time about it. Since 1987, most London pubs stay open between 15.00 to 17.30. Nicholson's Pub Guide states that you must buy food during these hours, but I do not think that is true anymore. At one time they were closed during these hours, by law, and some country pubs continue to close at this time. As of September 1995, the Sunday afternoon closing has been repealed, but that does not mean that all pubs will be opened.
All times are Greenwich Mean Time.
The underground is a good way to zip across town fast. The first thing to do is buy a pass, at any station. At this writing they have a one day and three day pass. This is better than having to queue to buy a ticket each time you enter a station. You will also need your pass or ticket to exit.