The Left Wing Immigration - Unemployment Paradox

In a conversation with a left leaning friend of mine I raised the idea that two main left ideas may well be incompatible.

Basically we were discussing unemployment and particularly his belief that most people who were unemployed wanted a job but that there were simply not enough jobs available for them - and therefore that Labour's new jobs for kids policy is set to magically solve unemployment. This led me to question another conversation we had at an earlier date that immigration is not detrimental to the UK, particularly the lower paid sections of the country.

My argument went that if as he claimed the majority of people that are unemployed want to work and are therefore unable to work as there are no jobs available then it stands to reason that one contributing factor is immigration, in fact with unemployment standing at 7.1% and foreign born (Employable) residents of the UK standing at 11.5% it necessarily follows that unemployment would be solved if it wasn't for immigration.

However if Immigration isn't an issue and the immigrants are coming here and doing jobs that nobody else wants then it necessarily follows that the unemployed are at least partly unemployed by choice. It should be a case that it is always easier to hire local staff over foreign staff as they have the language, cultural and society awareness that will aid in training and working life.