If he's at state primary now presumably you'll be looking at moving him for Year 7?
Most schools will need him to be at county standard for team sports like cricket and rugby and higher for individual sports like tennis or swimming as they simply don't need so many children to make up a competitive team. To get to that standard it would mean belonging to a club outside school as the standard of school sports especially at primary level tends to be lower
If your preference is for day schools you need to look at location and work out how easy it will be to get your son there and back bearing in mind that he will probably have to practise after school and have matches at weekends etc
Then you need to look at which sports the school excels in - e.g. hockey at Kingston grammar, tennis & cricket at Reeds, rugby at Dulwich, pretty much everything at Whitgift. Of those you then need to work out which would be the best fit for your son academically - obviously if he's absolutely astoundingly brilliant most schools will lower the bar if need be but it's not much fun being in the bottom sets of an über-academic school however sporty you are if your talents don't lie in that direction
Then you need to work out how much you can afford and whether or not you'd need a bursary as well - although some schools have sports scholarships of 'up to 30%' the vast majority of awards will be in the 5-10% range, nice to have but it's not going to make a substantial dent in the fees
The only sporty boarding school I know anything about is Millfield as we briefly considered it for ds1 - for his sport scholarships are awarded on a sliding scale depending on how far within the national qualifying times you are which means that to get 50% off the fees you'd need to be on the top 5 at your age group nationally and STILL have to find another £15,000+ a year. Millfield is also not particularly academic and full of exceptionally rich children ...
The other thing to bear in mind is that your ds is only 8 and may well change in the next few years - at ds' primary there was one boy in his year who was outstandingly talented at both tennis and football - was on Chelsea academy plus a G&T programme provided by the LTA - I bumped into his mum when he was about 13 and asked how he was getting on and he'd given up both sports in favour of music ...