Citizens of European Union (EU) countries can live and work in Britain freely without a visa, but non-EU residents need a permit to work legally. This can be difficult to obtain without the backing of an established company or employer in the UK.
Also, visitors from Commonwealth countries who are aged between 17 and 27 may apply for a working holiday-maker's visa which permits them to stay in the UK for up to two years and work on a casual basis (ie non-career oriented). These certificates are only available from British embassies and consulates abroad, and you must have proof of a valid return or onward ticket, as well as means of support during your stay.
Commonwealth citizens with a parent or grandparent born in the UK can apply for a Certificate of Entitlement to the Right of Abode, allowing them to work in Britain.
An option for citizens of some non-commonwealth countries is to visit on an 'au pair' placement in order to learn English by living with an English-speaking family for a maximum of two years. Au pairs must be aged between 17 and 27, and come from one of the following countries: Andorra, Bosnia-Herzegovina, Croatia, Cyprus, Czech Republic, The Faroes, Greenland, Hungary, Macedonia, Malta, Monaco, San Marino, Slovak Republic, Slovenia, Switzerland or Turkey. This can be a good way to learn English, but check out the precise conditions of your placement before taking it up.