There are an abundance of very good primary schools in Cheltenham with many having attained 'outstanding' Ofsted reports. I would house hunt first (never easy to find a house that you actually like when narrowing down a search to one particular area, you can guarantee you'll fall in love with a property the opposite end of Cheltenham than your preferred school!) then explore the radius of primary schools in that local area with a place for your DC (some particularly excellent schools may not even have a place) and go and visit the school. I don't think you apply for a primary school within Gloucestershire without proof of tennancy /completion statement (or I seem to remember we couldn't anyhow when we moved here in Dec last year) as it can come down to catchment etc if more than one child is applying for the same school place. Feel free to message me if I can be of further help. Having recently made the move to the county from Wiltshire I have been through the (very stressful!) process myself.. Good luck!
Thank you all. I really appreciate the advice from you all.