View from another Londoner. Don’t even bother trying to drive. We’ve woken up this morning to find someone’s been playing a weird game of Sim City with our road layouts.
My rec would be to dump the car at Luton Airport if you must drive, leave it in secure car parking overnight if needed, and train in. You’re going to need to be there early though, I think, if you’re in the Mall, so check train times carefully. I’m pretty sure they’re regular running cos it’s a ‘London airport’ thought it is of course blatantly not.
Otherwise, I’d take the train from Stockport but good luck getting a decent priced ticket, Virgin ram the prices right up the week before travel. Use Red Spotted Hanky and Tesco vouchers if you can to get a discount.