Most countries have different rules re visas and working agreements. In EU countries, only those who are citizens of another EU country can work and study here without visas. However, some visas are issued to foreign nationals who have skills that this country requires, eg some engineering disciplines, nursing and other medical professions. It is probably the same for all of the EU countries, whilst Switzerland and others who are not in the EU may have completely different rules. If you did manage to get a student visa for the UK, the rules are that students may only work for 20 hours per week and show sufficient funds to keep themselves and pay fees.
Here's the UK's Home Office site
http://www.ukba.homeoffice.gov.uk/visas-immigration/do-you-need-a-visa/