Uh ok. If your wife's clothes need to be 'personally' handled by her as she puts them into the commercial machines that will probably shrink them that's fine. But I truly don't get the I must do it myself thing. Presumably you're doing the undies in the hotel room, so it's just regular clothes being picked up/dropped off. Not like it's her knickers.

I like to experience lots of things in London as the locals do, but I can say traveling in multiple countries over multiple years sitting next to the washing machine/dryer, whether in London or other cities, just isn't my thing. If there's a pick up/drop off that's cheap I'd go for that - and then go sightseeing or out to a great meal whilst my laundry was being done.

BTW - you might want to ask the Londoners who 'don't have any choice', that 'if they had a choice' would they still sit there next to the machines. My guess is their answer would be a resounding heck no

But if you must give up your final afternoon or evening, might I suggest you pack a picnic to help you while you're waiting? You could get a bottle of wine, some cheese/crackers or other munchies & make it a bit more fun

Cheers.