I'm a Russian citizen, but I study in England and have a Tier 4 Student Visa. Can I apply for a Shengen tourist visa here, in England, without going to Russia?
Yes. In fact you can obtain the form online both in English and Russian.
Then follow the process on how to decide which consulate to apply to - but since most of them are in London, you should almost certainly be able to visit one of those, or adjust your plans slightly so that you first enter a Schengen country which DOES have a consulate in London :)