You should not travel to the UK or begin a course of study without making sure that you have enough money to cover all your academic fees and living expenses. It is virtually impossible to make arrangements for financial support once you have left your own country. Also, the immigration authorities will not normally allow you into the UK unless you have evidence that you can cover the costs of your proposed study.

Here are some resources available for Bulgarian applicants:

The Weidenfeld Scholarships and Leadership Programme
The Weidenfeld Scholarships and Leadership Programme is expected to support up to 40 Scholars in the 2010-2011 academic year.  This Programme, launched in May 2007, offers outstanding postgraduate students and young professionals, primarily from Eastern Europe, Russia, Central Asia, North Africa and the Middle East, support for graduate studies at Oxford University complemented by a comprehensive leadership development programme.
Detailed information is available here.
Find out how to apply.

Graduate Scholarships at LSE
Scholarships are available for students from Bulgaria starting a postgraduate programme at LSE in 2009.
More information is available here.
For details of all the latest information on how to apply see the LSE Financial Support Office site: www.lse.ac.uk/financialsupportoffice