Any of the websites mentioned above could be a good way of finding possible employers - see the section below. If employers are recruiting it could be worth asking if they would be prepared to take you on as an apprentice.
Networking is about using or developing contacts - friends, neighbours, relations or friends of neighbours and relations - to find a suitable job. Networking is the way that many people in senior positions find out about vacancies that never get advertised. It’s about promoting yourself and your abilities to others so that a company may decide to create a new job just for you or may think of you if a job becomes available. But there is no reason why you should not use the same technique to find an Apprenticeship.