Self Serve Laundry

I would ask your host or check Google maps
https://goo.gl/maps/2G6Q8PMtHrF2

Laundromats in the UK are called "laundrettes." You might want to search for them on Google Maps.

Here is a website with all the Launderettes in the UK
https://www.thomsonlocal.com/search/laundries-launderettes

Mayfair and such places as laundrettes don't normally travel in the same circles.

Big fancy car dealers and Shepherd Market are more like it.

If you are staying at the Washington perhaps you could ask them.

If you are staying there for a week just get the hotel to do your laundry. Also, I used Google Maps for the Mayfair District. There are numerous laundry's in the area, just drop off your laundry one day and pick it up the next. That is mostly how we handle it now on our trips. Other than the laundry we do in the sink.

Consider a service that picks up and delivers laundry. I used one a couple of years ago (can’t remember the name) They’re very common in urban areas, there’s a couple in Chicago. Look on the tube for adverts and probably a discount code for a first time user. Laundrettes are getting rarer with sky high London rents.

If you would be staying in an hotel, there just might be laundry arrangements within the hotel. You might want to talk to the hotel staff about it.