Answer:
The University of London is a federal institution: the University (Senate House headquarters) determines exam standards, awards degrees, & maintains certain facilities/ specialist research institutes etc., whilst academic teaching & research are conducted by the various constituent "colleges".
These constituent colleges vary considerably in size & character: some have a specialist focus & are relatively small (eg London School of Economics - social sciences, law etc; Goldsmiths - arts, design etc; Heythrop - theology/ religion, philosophy etc; Birkbeck - part-time study for mature students; Institute of Education - education; the Royal Veterinary College - veterinary medicine), whilst others are much larger (probably 20,000 +), & are, in fact, comprehensive universities in their own right covering everything from arts/ humanities, social sciences, languages, maths & science to engineering, law, medicine & dentistry, & business.
Such "colleges" include University College, King's College, & Queen Mary College. UCL & King's are the oldest (and arguably most prestigious) - the "foundational" colleges of London University. Royal Holloway is another - located at Egham, Surrey, on the fringes of London proper: originally it was a female only college. Today Royal Holloway is co-ed, & covers arts/ humanities, languages, sciences/ maths, social sciences etc, but not engineering, medicine, dentistry.
St George's, South London, is a very big medical school/ centre for health sciences: teaching & research are entirely medical & health science focused, including nursing, podiatry, optometry, physiotherapy, as well as its large medical school.
Imperial in South Kensington (science, maths, engineering & technology, medicine etc) has recently (2007) left the University of London federal structure, & is now a separate university in its own right, awarding its own degrees.
There are also numerous research institutions under the London University umbrella - eg Institute of Historical Research; specialist schools of Oriental, African, Eastern European, French & German research; various medical institutes (eg Cancer Research; Tropical Medicine & Hygiene); the Courtauld Institute (Fine Art/ Art History), as well as the School of Pharmacy, & the London Business School.
London University is huge: if "external" students (ie students studying for certain degrees via distance learning or in associated institutions abroad or elsewhere in the UK - law & economics are very popular) are included, it has well over 170,000 students. On a practical day to day basis, however, most students live & study in the individual colleges to which they belong, & the University of London is simply the overarching authority that awards degrees. UCL students will, therefore, spend their time in & around the University College campus in Bloomsbury/ Central London; Queen Mary students will be in the rather different environment of the East End, whilst those at Royal Holloway will be in the very wealthy, semi-rural, environment of Egham, Surrey... but all are students of the University of London.