Hmm. I wonder if the problem has got worse compared with pre-Pandemic? Despite all the much-publicised expectations about Crossrail, is it really encouraging Twyfordians to venture into Central London?
I would suspect that Twyfordians are not the issue with people parking in the street in Twyford.
There are a lot of people who live a car-based life living to the west of London in communities with little or very limited rail service who never use their local trains, but on occasions visit London and would never dream of taking their car all the way in.
There have been a number of park-and-ride favourite in the past - ranging from Osterley to Bedwyn but local stations on the Reading to Paddington route wouldn't have made a "top ten" list. Price of parking, frequency of service, cost of tickets,ease of access of the trunk road network, and directness of service into central London are all factors.
Twyford now has (I think) a sevice every 15 minutes or so DIRECT to the West End (Bond Street and Tottenham Court Road) and the City (Farringdon and Liverpool Street) as well as further east. Very attractive; the whole yucky business of standing around in Paddington waiting for the next service on a night likeliest night is gone. So I suspect the uptake at these stations has been not a consequence of covid in any way, but rather the sponge effect of the Elizabeth line doing - err - exactly what was intended!