Hmm, I do West Norwood - Brick Lane, which is half of Steatham - Westminster. I also used to commute West Norwood - Marylebone, which is probably even closer to what you want.
I would be tempted to go down Brixton Hill (in the bus lane - obvs), past Stockwell, Up Vauxhall and tehn down Albert embankment. The only problem I ever have is coming back up Brixton Hill of an evening as this is apparently where all teh angry morons congregate. The rest is fine. This'd take about 30 - 45 mins, I reckon.
If you fancy a bit of a longer ride, a much nicer ride is to go down the back roads to Clapham, then from there down the back roads to Battersea, over Chelsea bridge and down embankment to Westminster. Always fond of that route. This one'd probs be round an hour - an hour fifteen.