You and the owner (or management company) should have the only keys to the flat, unless you're getting maid service or something like that. So your stuff should be safe enough there. But if I were you I'd carry my cards, major cash, and passport on my person, in a money belt or neck wallet, all the time I'm outside the flat. Put a little cash in a pocket for routine spending and keep the rest under your clothing. Use a debit card and ATMs to replenish cash every few days, having notified your bank of your plans so they won't cancel the card when they see a London transaction.
If you have "valuables" beyond cash and cards, like expensive jewelry, leave them at home.
And, btw, please share with us how you mastered time travel, to be staying in a London flat in January 2014! ;)