Um, aren't those graphs a little disingenuous? The first one for not taking into account the population size differences and the second for not showing UK employment alongside it?
For the first graph, I'm not sure that's really relevant? Over the course of that time, the UK population wasn't falling. Unemployment for British nationals was static or going upwards from 2000 onwards. And the graph shows that the number of British people in work was falling, where as the number of immigrants in work was going up. If you need some more data let me know and I'll try and find it, but I can't really think what would have to be happening elsewhere for this graph (along with the knowledge that both British unemployment was stagnant or rising from 2000, and the total British workforce population was increasing) for it not to back up what I was saying.
For the second graph, I'm not sure why you need to see UK employment alongside it - that graph plots the percentage of the UK's workforce that was born outside of the UK. To find the UK employment, it's just 100 minus that number at any given time. In 1997, approx 7.5% of our workforce was born outside the UK. By 2007 it'd almost doubled, up to 13%. Now, evem with the (easily discernable) British figure, this still doesn't tell us everything - it's possibly that UK demand for labour was outstripping the UK's ability to provide labour, and thus overseas workers came. However if you take a look at this graph...
We see that they were both rising more or less in parity. As we can see
here, between 2000 - 2008 our unemployment level remained more or less static (at a very low 5% - it should be noted that that figure was massaged quite significantly, but that's for another discussion - the point is that 5% is, whilst low, higher than the 2% that is considered 'full employment', and thus there were certainly people out there looking for jobs that could not find them), though it started going up at around 2005. However, even this doesn't prove my theory - afterall, the immirants coming to the UK could have been doing jobs that those 5% were not skilled or equipped to do.
What does lend a lot of weight to my argument, though, is from 2005 until now. At this point, UK employment numbers in real terms are actually going down, yet immigration employment figures are going up. This 2005 number coincides with the above note that this is when UK unemployment (which doesn't take into account immigrants in the UK without a job) began to rise. In other words, from 2005-2012, immigrant employment levels have continued to rise, British employment levels have continued to fall, and British unemployment has continued to rise (save for a blip in 2008) .