If you are being cost aware, or just prefer to use public transportation, get an Oyster Card. An Oyster card is a prepaid fair card for the Underground and buses. It costs a £3 deposit, plus any fair you choose to put on it. The system automatically calculates the cheapest ticket combination for whatever travel you do. Therefore if you only use it for a single trip in day, it debits for that trip, however if you use it several times, it debits up to the cost of a day pass which is much cheaper than single tickets. When you leave you can return the card and get refunded the deposit and any fair on the card. If you are fly in and out of Heathrow Airport, there are kiosks in the airport for the cards. If you are flying into Gatwick, you can take the train from the airport to Victoria Station which will also have kiosks for the Oyster card.
Also don't bother using currency exchanges. No one ever seems to change enough, and if you change too much you can get burnt converting the extra back. You can use your bank's ATM card in the cash machines here. Don't take out too much cash, just a little pocket money for the occasional taxi or ice cream cone. For all other purchases I recommend using a credit card for purchases for the fraud protection (usual warnings about knowing your financial limits apply.) Some ATM, Debit, and Credit card providers block foreign transactions by default. You can usually contact them and explain you will be traveling to specific countries on specific days and will remove the block for you. This usually isn't a problem in the UK, but its worth checking anyway. Definitely check with your banks if you plan on making a side trip to France; everybody seems to block French transactions.