I’m not an upholsterer but have plenty experience of them and office chairs. To reupholster in leather you will need a decent quality leather to upholster the curves, if you have to buy a hide then you’ll be looking at a few hundred for that never mind the upholstery cost. I would use a good quality vinyl or PU (this is softer and more flexible) which will cost you a lot less.
For a good quality PU I would suggest camira deca https://www.camirafabrics.com/en/fabrics/contract/deca most upholstered should an have account with them if they do office seating.
I don’t know any upholstered in Nottingham I am afraid.