I think these pages answer your questions:

http://www.westminster.ac.uk/interna...erm-study-visa

http://www.lse.ac.uk/study/informati...ntvisitor.aspx

The following applies only if you don't normally need a visa to visit the UK.

If you intend to apply for your study visa at the airport rather than in advance (note that it appears the visa on arrival is free), then why don't you just ask the immigration officer when you arrive? You can show all the documents to explain your situation but still ask for leave to enter as a visitor.

My opinion is that it would be inappropriate to issue you with a short-term study visa if you are not going to study for your initial visit of 1-2 days, as it would become invalid as soon as you left the UK for your European trip. So you should be granted leave to enter as a visitor initially. However, you would need to bring all the documents along during your Europe holiday, and if they were lost you would not be able to re-enter the UK.