I'm 3 weeks into a 6-week trip to the UK. I do carry-on, so laundry is a must. So far, I've done it myself twice, had it done for me once and washed one pair of pants in the shower (no tub and sink too tiny to wash them in).
I had it done in Bath: wash, dry and fold, all in one load, picked up in the morning at my B&B and returned at the end of the day. Cost was £14, the same as if I'd taken it to the laundry to have it done.
I did it myself at a laundry about a 15 minute walk from my B&B in Edinburgh. I could have had the attendant do it, but she was swamped, so it was faster for me to do it. She helped me and I was completely done in about 1.5 hours. Cost was about £7.50. I didn’t write it down because I was so entertained by the attendant. It was the time of day when primary kids got out of school. They'd stop in and get a wee biscuit on their way home. Just one. She'd make them put the extra(s) back if they took more than one.
Edinburgh is also where I washed the pants (the ones I was wearing while doing the laundry) out in the shower. I rolled them in the bath mat, stood on the roll to squeeze out as much moisture as possible and hung them on the hot towel drying rack overnight. They didn’t dry completely, but by shifting them around a few times while I was awake, they were dry enough to hang in the closet to finish drying over the next day.
I also did laundry at the new Laundrorama in Kirkwall on Orkney. Great machines. No place to sit. You have to buy tokens from the attendant. Total cost was £14.40. This was the busiest self-service European laundry I have ever been in. I'd guess 1/2 were tourists, including the couple from Seattle who knew someone there I also know.
So that comes out to about once a week. I won’t do it before I leave Aberdeen on Tuesday
If you pack for a week and a day, you should be able to do laundry only 2-3 times on your trip. Your lodgings should be able to tell you where you can do it or have it done, but I agree that with limited time, doing a little in the evening or having it done by your lodgings might be worth any additional expense.