http://www.telegraph.co.uk/finance/p...her-shows.html
Tesco/Sainsbury's sandwiches are much cheaper than M&S or Pret. If you stay at a hostel, you should have kitchen facilities available so you can also make/share cheap food.
Oyster card is an obvious money saver - it will automatically decide the cheapest ticket for you, i.e. if you take individual trips where the total price exceeds a day ticket, it will just charge you the price of a day ticket.
$1000 for 10 days is doable. For reference, as a student, I stayed within my €500 per month free-government-money almost every month if you exclude accommodation. As you can get a bed in a central (Kings X etc.) hostel for $20-$40 per night, you still have more overall spending money than I used.