The Tier 4 student visa you will obtain to study on the General Course will enable you to undertake paid work for up to a total of 20 hours per week in term time, and full-time during vacations. Many General Course students take advantage of this opportunity in order to increase their living/social/travel funds.
The LSE Careers Service works with General Course students to offer advice about internship opportunities in London. Seminars are frequently held specifically for General Course students on this topic.
LSE itself employs many students on a part-time basis, for example as event stewards, office assistants and in the Students' Union bars.
There are also many opportunities for voluntary work at organisations such as Barnardo's, a leading UK children's charity, and FoodCycle, who run volunteer-powered community projects.