For Primary (my DS recently started):
2 school jumpers with school logo
3 pairs trousers
5 pairs plain black socks
1 polo shirt with school logo
1 plain shirt (not official uniform but DS will be at this school one term max and it's the right colour)
1 PE kit (Logo Tshirt and shorts)
boring school shoes and PE shoes
School book bag and PE bag (required at DS's school)

All the official stuff is logo'd so you can't re-use it outside of school or if you move schools, which is annoying. And is also why I let DS wear shirts to school - they're the right colour and a jumper covers them: I am just not spending a tenner on a polo shirt that is going to be worn just 10 weeks. Thankfully we got a lot loaned to us second-hand, and the new stuff I needed to get is getting gifted to the person who loaned us the uniform when we move.