Can a UK passport holder enter Thailand for 45 days, extend for 30 days, and re-enter after a short trip to Laos?

Yes you can but you should fly, not cross by land.

can you get a 45 day exempt when you cross friendship bridge from Laos instead of flying ?

What you proposed is perfectly fine- enjoy.

Better You Fly to Holland

From 1st of October you get 45 days visa exempt , you can extend that once at immigration for 30 days then do 2 border runs for another 90 days ,(45 each jump) or if you have the financial proofs just go & get an elite visa for 5 or 10 years 🤙🏼

45 day visa starts October 1st

In theory at least what you propose should be possible.

First of all you need to use the correct terms. UK passport holders cannot get visa on arrival. They are eligible for visa exempt, which means NO VISA at all. There is no 45 day visa. It would be visa exempt.

Now in terms of replacing a non-O with visa exempt, it depends on how long you are planning on staying in Thailand. There is no official limit to how many times you can get a visa exempt (except you can only do it by land border 2 times per calendar year).

That being said, after your 3rd or 4th time, passport control is going to start asking you why you are maxing out your stay every time, leaving for a few days, and then coming right back. Eventually they are going to deny you entry, as it will appear you are living in Thailand on a method that is meant for tourists. If you want to live in Thailand, you need an appropriate visa for that.