I also had a bad fit with my first driving instructor. He was a rather older man who seemed kind of patronizing. And he treated me like a new driver (started with how to make the car go!), even though I made it clear from the beginning that I'd had close to twenty years experience driving in the US and only needed to be told what I needed to correct to pass the UK test.
My next instructor had provided lessons for another American and understood what I needed. We did three 2-hour lessons, where she took me along all the known places in my area and taught me what I should look out for during my test, and she taught me the "right way" to do the manuevers, and helped me feel comfortable on the opposite side of the road driving from the opposite side of the car. I also booked her/her car for my test, and all together it cost me about £130 for lessons, plus the various DVLA fees along the way.
I did my theory test before we moved, and in the old location, I had about a six week wait to get a test slot. We moved to a rural area after that, so I had a pause in my UK license pursuit. Once I was ready to get back to it, I know I did my exam at theend of April that year, and I think my first lesson was early March, so probably about a six week wait for that, too. But, again, it's a pretty rural area. More populated areas will have longer wait times. And right now, with the Covid backlog... ugh, I wouldn't like to guess.