Hi
I wish I had enough money to have a string of properties to rent out to USA movers coming here! but I don't, as you may well know, property pricing is beyond insane in the UK!
I'm a private landlord and as I'm such a good one, my tenants stay long term and I look after them with whatever needs doing (which isn't much!)
I can only suggest to keep scouring the local ads in gumtree, and when you do choose an area to live, the local shops with cards in the window, and also local newspapers and property publications. Private landlords do exist! all the ones I know with plenty of properties to rent are all out this way in Slough and other just outside london areas, so no good for you!
Good luck! Cheers, DtM!