Car Parking at the Brompton is very restricted and street parking even with a Blue Badge is not that easy if you have to park some distance away.
I can recommend a site called JustPark, you can find the nearest location to where you need to go and the cost, whilst it is not cheap, its better than parking some where and then overrunning and getting a ticket
For the Brompton there is an underground car park by the Metro Bank in Sydney Stree with a bus stop acroos the road or a taxi costing about a fiver to the Fulham Road, downside is it is a bit murky and a tight downward descent but Ok
Another much nicer one is the Gloucester Millenium Hotel, they will park your car for you and taxis are waiting in the hotel entrance
You can search all over the UK and its not only car parks but peoples drives as well
I use the ones mentioned above for the Brompton