About an hour if you avoid traffic jams/tunnel closures - I'd go via Rotherhithe tunnel, then left and left and left again into the Limehouse Link tunnel which takes you right to the bottom of the A12 (follow signs to Blackwall, weirdly) and then it's dual carriageway/motorway all the way. Worth checking before you set off whether any of the tunnels are closed - I've had a couple of trips turn into frantic panicky dashes because Rotherhithe was shut. If you're going for more than a week or so, it's worth considering a minicab - about ?45-?55 each way, compared to about ?50 for the long-term car park plus petrol costs if you drive, and it means you avoid the 45 minutes or so each way waiting for/on the shuttle bus.