"Weather too prohibitive to enjoy..." I don't even understand the question, frankly. ;-) Seriously, London is an AMAZING and FABULOUS city and no amount of sleet, drizzle, hail, dust devils, water spouts with sharks, or invading hordes of kraken could possibly make it un-enjoyable!
Okay, in fairness, maybe the hordes of kraken would put a damper on things. But of course, London doesn't get those in March. Nor does it get much sleet or hail or snow. It is rather clement in March, there are sunny days and cloudy days, and if you don't fancy sightseeing outside if it's cloudy, there is sooooo much to do inside that you won't go begging for choice.