The London Pass does not entitle you to free use of public transport. But you can book a Visitor Oyster Card at the Visit Britain Shop, which allows you to use all public transport in London. This includes the London Underground, buses, the Docklands Light Railway, River Boats and local trains.
Instead of paying in full for each journey, your Oyster Card is loaded with credit which should be sufficient for your journey to London if you travel in the city centre (zones 1 + 2).
You can set the amount of credit yourself (£10 - £50). When you order the Oyster Card, you pay for the credit and an activation fee.
A portion of the credit is deducted for each trip, but there is a daily limit, which is usually reached after the third trip. Further journeys on the same day are then free of charge. When the credit is used up, you can top it up at a ticket machine.
If you want to order the Oyster Card by post, you must do so at least two weeks before your trip.