Another solution which I have used - similar to BEags' in a way.
I've used the Cockfosters Underground Station Car Park a lot. Not recently so I can't advise on current charges (yes I can - just Googled it) So it's £5.70 a day Mon-Fri, £2.60 Saturdays and Bank Holidays, and £1.70 for Sundays. That's cash price - cashless is a few pence cheaper.
It's the end of the Piccadilly Line, so goes straight to Green Park - about a 35-40 min journey, and change out of a fiver if you're paying full price....
That's the solution from the frozen North, I'm sure there are similar plots from other directions.