To give you a case study I’ll mention Caribbean immigration to Britain after the Second World War. During the war a fair chunk of British working age men were killed or wounded in the war, on top of this German bombing had damaged parts of British cities and infrastructure. There were a lot of jobs that needed doing but a shortage of workers.

In British Caribbean territories the schooling system and British wartime propaganda had placed a lot of empathises on the citizens there being ‘British’ and of the same status within the Empire as British citizens born in the UK. A lot of young Caribbean men had fought for Britain in the war and served or been stationed in the UK.

After the war with the shortage of jobs and the ease of being able to enter the UK, assuming you could pay for a boat across, led many Caribbean people to consider moving to the UK.

Sources: http://www.bbc.co.uk/caribbean/news/story/2008/06/080620_windrush2.shtml

http://webarchive.nationalarchives.gov.uk/+/http://www.movinghere.org.uk/galleries/histories/caribbean/origins/origins.htm

http://webarchive.nationalarchives.gov.uk/+/http://www.movinghere.org.uk/stories/default.asp (this one has a lot of recorded oral histories from migrants to the UK from various countries of origin)

To add a few qualifications to this answer though it’s incredibly hard to determine why an individual chooses to migrate. Conventionally we’ve looked at push a pull factors but there’s a rising trend within global history and migration studies that suggests motivations are far more complex than this.

Some good recent books on migration include:

James Belich, ‘Replenishing the Earth: The Settler Revolution and the Rise of the Angloworld’

Christiane Harzig and Dirk Hoerder, ‘What is Migration History’