The lump of labour fallacy rests on the (flawed) assumption that the number of jobs is fixed. This is not so as Jonathan Portes explains:
“The period of high immigration that began in the late 1990s actually coincided with historically very high employment rates for British-born workers,”
“The government’s figures show that from 2005 to 2008 the numbers of Britons in jobs actually rose – by 116,000. This was a period of near full employment in Britain with demand for workers often outstripping supply so it’s no surprise that employers turned to migrants to fill the gap. As a result the numbers of migrants in work rose by 660,000.
“It is not the case that migrants and British workers are just competing for the same jobs. In 2008, when migration was at its height, the number of unfilled vacancies was the highest ever recorded at 700,000.”