Um, The last part is complicated. Really speaking it is down to the skin, but in truth a lot of skin heads didn’t go that far.
The whole thing actually may have nothing to do with skinheads.
Schools in the UK often maintain standards of personal appearance along with the uniform. These often include rules about severe haircuts, hair colours, make-up levels, jewellery and if no uniform is set then the range of clothes you can wear. At my school a boys hair had to fall above his colour be un-dyed and be tidy.
These rules are a mixture of tradition, control, the fact that they lead to better behaved classes and about teaching fitting in to children. We are a reserved and repressed society and by teaching our children under these conditions it helps them to be a part of that society. It also achieves better grades, attendance, discipline and makes the school look better garnering better. This is wonderfully mocked in the Simpsons episode ‘Team Homer’ Where discipline and order at an all time high (the kids even walk between classes in step with one another and in silence) after uniform is introduced. However it stifles creativity and supposedly makes for repressed and dour children (all the better to fit into the subsequent society)
Simply put it is a part of British culture.