you are allowed to work, but you may find getting a job difficult because you are on a visa.

London is an expensive place, you can get a cheap place if you share with other students & live in cheap area http://www.findaproperty.com type in E16 or E6 there are plenty of cheaper places like E10 but that might be below your minimum standard for safety etc


just ask here if you want to know what specific areas are like