>>Possible Snow in the SE of England in March <<

??? Not terribly likely. There is just as much chance for nice (or awful) weather in Southern England as there is in France.

If you want to head north-ish/ west from London (like the Cotswolds and the Harry Potter studio tour) then flying to LHR makes most sense. If you want to see the south/south coast (Kent/Sussex/Hampshire.etc) the ferry makes great sense.

I took the overnight ferry from Oustreham (Caen's port) to Portsmouth - saw the famous Naval Ship Yards there - and took train to London - you can rent a car at the ferry dock to be waiting for you - large boat with lots of entertainments on board- book really early to get fares a lot cheaper than I did by just turning up and get a private room - I slept in the barely reclining 'pullman' seats and not so comfy and not so quiet.

daytime catamarans were doing Cherbourg-Southampton for 29 pounds and those only took I think a few hours - overnight ferry saves on cost of hotel too.