The cost will depend on various factors like what you will be eating, cost of transport and whether you will be doing any shopping. When it comes to eating, a decent sandwich will set you back around ?3. A good meal for one with wine usually costs around the ?40 to ?60 mark. Even if you have accommodation, you might end up using about ?500 and ?1,000. See www.lonelyplanet.com/england/london/practical-information/money-costs for details.
During Desert Storm, our hospital went to England as a 4th echelon treatment facility. A slice of pizza that would cost a couple of dollars here cost about $14 there. The price of everything was crazy compared to our own. Desert Storm was in early 90s.... so I am certain it is worse now.
One other expense, get your antidepressants filled here to take with you. It is very cloudy and dreary most of the time in London. Depressing. I would get all my meds filled here before you go. (If you take antidepressants or any other RXs.)