It amazes me that almost all of the problems mentioned here which prevent British people taking jobs do not seem to prevent immigrants from doing so. With the possible exception of age (no, I would not expect most 65 year olds to spend their days picking vegetables) most of the other problems mentioned are surmountable.
However, this problem is not one exclusive to farm work. Many of the "menial" jobs in the hospitality trade are now done by immigrants, mainly (though not exclusively) from Eastern Europe. I spent last weekend in a very pleasant village pub in Sussex. Three of the four bar staff were eastern Europeans, most of the waiting staff were too and the chambermaid (there were only eight rooms and she did them all) was from Poland. Speaking to the governor over a nightcap he was at pains to explain that his jobs were well paid (he paid more than the minimum wage, his staff shared all the tips which were not inconsiderable, and a few positions were “live in”). But he simply could not get young Brits to do the work. Most of them simply will not work in his trade as it means them working when their mates are out getting bladdered or, with their degree in Media Studies, they considered the work beneath them.
Agreed, some older people do face some difficulties getting work, but there are huge numbers of young unemployed people in the UK. Excluding those in full-time education, there were 489,000 unemployed 16-24 year olds in May to July 2014 and 200,000 of them had been unemployed for more than twelve months. Young people can travel from the far end of the continent (and beyond) and soon find themselves a job and somewhere to live. The reason many young British people don’t take these jobs is because it suits them not to.