This commonly said statement would be hilarious if it wasn’t such an indictment of our own stupidity. Let me explain using data from the 2001 UK census.
According to the 2001 census, the population of the UK was 58,789,194, (it has since risen to roughly 63 million). Of that 58,789,194 figure 50,366,497, identified themselves as being White British, meaning that in 2001 roughly 8.5 million people were either recent immigrants or their descendents.
Under the census section titled "work", only people aged 16-74 were considered. There were 42,525,596 people in that age bracket.
Employed 25,620,559 (43.58%)
Unemployed 1,458,523 (2.48%)
Other* 15,446,514 (26.27%)
Total 42,525,596 (72.33%)**
* Other Is made up of such categories as, students, the retired, permanently sick/disabled, looking after family. See http://www.statistics.gov.uk/census2001/profiles/uk.asp for a full breakdown.
** The % figures are for the total population; with the remaining 28% being people aged 0-15 and 75+
If we use the same logic as used by those stating immigrants take our jobs, then we can say there were 1.5 million unemployed, and 8.5 million immigrants, therefore without those immigrants we would have 7 million more jobs than people. That is clearly absurd, what actually is being demonstrated is that for every additional person living in the country, their increase to the economies aggregate demand results in additional jobs. Whether that additional person comes from natural growth or immigration should be totally irrelevant as to the total number of jobs.
However that is not the case, there is a difference in employment levels between ethnic minorities and those classified as White British. When looking at Unemployment rates by ethnic group and age (Men up to 64 and Women up to 59) the unemployment rates for white British are lower.
What this means then is that immigrants come over here, create additional jobs (by virtue of their need for food, housing, clothing etc), for the most part filling those jobs, but with a disproportionate amount of the jobs they create instead going to the British unemployed.