Your numbers don't add up. You live in a premium location, I guess a nice part of zone 2? So let's say 1mn GBP for a 3 bedroom house.
You pay 20k/year in rent (2%) = 1666/month for a 1mn property?
Then you're getting an incredible bargain. You can only get a 1 bedroom flat for about that in a good part of London. A 3 bedroom house would be closer to 3k/month, so really you're looking at 4-5%/year. So the difference in performance is only 2-3%, which would be offset by the gains you'd make in house prices from owning your own place.
That's not possible, you're not getting a place for 2% of purchase value on the open market. There are no £1mn properties available for £1,666/month, or £500,000 places for £833/month, it's more than double that everywhere in London
You pay 20k/year in rent (2%) = 1666/month for a 1mn property?
Then you're getting an incredible bargain. You can only get a 1 bedroom flat for about that in a good part of London. A 3 bedroom house would be closer to 3k/month, so really you're looking at 4-5%/year. So the difference in performance is only 2-3%, which would be offset by the gains you'd make in house prices from owning your own place.