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 Overseas Research Students Awards Scheme
(ORS) grants awards on a competitive basis to international postgraduate research students of outstanding merit and research potential. The award scheme is administered by Universities UK on behalf of the Department for Education and Skills (DfES), and is reimbursed by the DfES through the UK funding councils.
Research Students Awards Scheme (ORSAS): www.universitiesuk.ac.uk/ors/

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