You can apply for a UK passport if you are not resident but in the UK long enough for the passport to be delivered. I just did it for my daughters and although we left before they turned up they are safely with family.

One caveat is that if this is the first passport (looks like it is for you) then you need to have a certified photo, which might be harder for you to do. I was renewing.

I agree the application fee for overseas residents is excessive.