Many posts on this site mistakenly assert that the UK work visa system means that MBA candidates from outside Europe should rule British business schools off their list and, instead, focus only on mainland Europe. In fact, the top British business schools continue to be some of the world's best at placing international students. Nine of the 20 best schools for international mobility are from the UK: Best schools for international students' placement http://www.find-mba.com/board/41143
The UK offer several routes into work. Work is possible during your studies, and UEL has a good summary here: http://www.uel.ac.uk/isa/working-in-the-uk/
When it comes to working after studies, the UK council for international student affairs has a good summary here:- http://www.ukcisa.org.uk/International-Students/The-next-stage/Working-after-your-studies/ Cambridge summarises the routes in an easy-to-read table: http://www.internationalstudents.cam.ac.uk/visas-after-studying
A key time limit is that students can stay for only four months after their studies, as outlined here: http://www.workpermit.com/uk/uk-immigration-tier-system/tier-4-foreign-students.htm This is, in comparison with the prior work permit system, unclear, unfair and unjust (http://www.theguardian.com/education/2015/apr/23/are-international-students-getting-a-raw-deal) but many students are still able to find work. Of course MBA students, with their higher salaries and greater value, are very likely to find work. Indeed, the FT rankings show that very many students are able to find work within three months. It's certainly an advantage for longer programmes like LBS and Alliance MBS that students have more time to find work.
For more information, the LSE has published the slides of its two workshops on the question at http://www.lse.ac.uk/intranet/students/ISIS/currentStudents/Workingafteryourstudies.aspx and that page includes more details on the pathways.
Indeed, these different routes are more cumbersome than a guaranteed right to remain however the added advantage of English as a home language and the long presence of non-Europeans (especially from south Asia, Turkey and Nigeria) means that the UK remains well above the average in terms of the numbers of non-Europeans who find work here.
PS Find MBA has a great article on this topic at http://find-mba.com/articles/uk-visa-issues-staying-in-the-country-after-an-mba
[Edited by Duncan on Nov 27, 2015]