Parking is a little bit tricky, I have never seen an event of any description that included parking in central London, just not practical. Events use all of the space they are allocated for the event, not punters cars. I'm guessing this will be a weekend event so not so much of a problem. Also no congestion charge at the weekend.
Saturday parking restrictions are relaxed a bit, some multi stories are cheaper. Sunday, restrictions relaxed more, (apart from near markets etc.) more free spaces.
Public transport is very good, generally, park further out of town and use that.
I wouldn't even worry about the police, as long as you aren't waving your gun about they won't care.