Marvin,
There are jobs available although there are a lot of applications for each vacancy and they are not all in London. The best places to look are Design Week weekly (http://www.mad.co.uk/publication/dw/) and The Guardian on Monday and Saturday (http://jobs.guardian.co.uk/) or online nb. design week requires registration which you can have for a free trial period. You will need samples of print items, pdfs are not always acceptable, nearly all job vacancies require samples of work to be sent with your application. There are also temp agencies like http://www.workstation.co.uk/ who have full/part time vacancies and freelance work. Aquent was reckoned to be one of the best but I have had no experience of them http://Aquent.co.uk/.
Good luck
Tim