Why did Britain decide that it needed a m wave of immigration from the Commonwealth nations (1950s onwards)?

In part, there were no restrictions on immigration from the Commonwealth/Empire and people in poor countries with very little hope of work and advancement saw opportunities in the UK. For a fictional take on this read Andrea Levy's 'Small Island' which was televised on BBC a few months ago. Also, there was a shortage of labour in the UK - for example, London Transport had recruiting offices in the West Indies. Frances Empire was nothing like as large as the British Empire.