I'm a Russian citizen, but I study in England and have a Tier 4 Student Visa. Can I apply for a Schengen 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 :)
Mark Mayo's answer is the canonical reference point for your question. I wanted to add some of the legal groundings for why this is so.
You will be able to apply for a Schengen visa at any of the member consulates in London using one of these as the enabling factor...
Normal residence: Your T4 was issued for a period of more than 6 months giving you the claim to 'normal residence' in the UK for visa purposes (but not the claim to 'permanent residence'); or
Proportionality: Schengen members should accept applications where to do otherwise would be disproportionate. This is explained by example in the Schengen Handbook...
If both of these fail, then the consulate is out-of-line and you will be entitled to lodge a complaint.
Source: Commentary by 'Relaxed'