Please, for the love of all that is frugal, never just show up at Heathrow and expect a bargain. The on-site car parks will charge you the price of a small island nation. And the off-site ones? They’ll treat you like you’re desperate, because you are.
I once saw a guy pay £180 for a week of parking because he rolled up cold. Don’t be that guy. Be the savvy traveler who books online at 2 a.m. in their pajamas with a cup of tea. That’s the energy.