http://www.ukba.homeo...students/conditions/#
"The maximum amount of part-time work you can do during term time is:
20 hours per week if you are studying a course at or above UK degree level or a foundation degree course, and/or if you made your Tier 4 (General) application on or before 2 March 2010; or
10 hours per week if you are studying a course that is below UK degree level and is not a foundation degree course, and you made your Tier 4 (General) application on or after 3 March 2010.
You can work full-time during vacations, within the above limits. If you have completed your course and you apply to remain in the UK under the points-based system before your existing permission to stay expires, you can work full-time (within the above limits) until your application is decided."
If it were me working there I would have no issue in picking up the phone can calling the UK border agency