It's not impossible but you've got to try very hard. The main barrier is still the work permit. Getting a degree from one of the top schools, such as Oxbridge, LBS and LSE, will largely increase your chance of getting employed in the UK. Now the graduates from some of the top b-schools can apply for a HSMP vias which allows them to work in the UK without having to obtain a work permit.
It's really very difficult. Even you graduated from top european MBA school, it's still hard to find a full-time job. However, ther are some students getting that there. The probability is low, but not zero. Bless you.