Citizens of Australia, Canada, New Zealand, South Africa and the USA are given, at their point of arrival, ‘leave to enter’ the UK for up to six months but are prohibited from working without a work permit. If you’re a citizen of the EU, you don’t need a visa to enter the country and may live and work here freely for as long as you like.
Visa regulations are always subject to change, so check at www.ukvisas.gov.uk or with your local British embassy before leaving home.
Immigration authorities in the UK are tough: dress neatly and be able to prove that you have sufficient funds to support yourself. A credit card and/or an onward ticket will help.
Nationals of EU countries can enter the country to study without formalities. Otherwise you need to be enrolled in a full-time course of at least 15 hours per week of weekday, daytime study at a single educational institution to be allowed to remain as a student. For more details, consult the British embassy, high commission or consulate in your own country.
Tourist visas can only be extended in clear emergencies (eg an accident, death of a relative). Otherwise you’ll have to leave the UK (perhaps going to Ireland or France) and apply for a fresh one, although this tactic will arouse suspicion after the second or third visa. To extend (or attempt to extend) your stay in the UK, ring the Visa & Passport Information Line (0870 606 7766, 8649 7878; the Home Office’s Immigration & Nationality Directorate, Lunar House, 40 Wellesley Rd, Croydon CR9 2BY; 10am-noon & 2-4pm Mon-Fri; East Croydon) before your current visa expires. The process takes a few days in France/Ireland. Trying to extend within the UK takes a lot longer.