I'm in the same position as you, im just finishing my law degree but want to convert to quantity surveying. A good place to start is by searching for civil engineering firms and then looking on their websites (mainly the big firms) because they may offer a 'graduate scheme' where they take you on and pay for your conversion training whilst you work for them! also, try this site, has a boit of info on what they require, job description, salary etc
http://www.prospects.ac.uk/cms/ShowPage/Home_p age/Explore_types_of_jobs/Types_of_Job/p!eipaL ?state=showocc&idno=99&pageno=1 hope this helps, good luck to u!