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I doubt many 'socialists' want to restrict free movement. The main gripe is how employers depress people's wages by attracting labour from countries with much lower wages. Solidarity doesn't work if countries have vastly different standards--foreign workers aren't really scabs despite coming from far away and taking local labour. Corbyn has often said he wants to end that exploitative mechanism. The single market is all well and good in theory (although there is the problem that larger markets tend to favour larger companies), but when it's built on such (worsening) wealth inequality, it is certainly worth considering, from a socialist perspective, whether the interests of poorer workers would not be served better by modifying it. Obviously, to take the example of fruit and vegetable picking, it's likely that farmers actually would let the produce rot in the fields rather than attract local workers with decent pay for that work, but there's a problem with the whole supply chain--large supermarkets putting pressure on farmers to lower prices, consumers expecting very low prices for food, food getting trucked all around the country, flown in as air freight, trucked from other countries--it's a very big mess and a very skewed market.

Where I grew up in Germany, the local food system still just about works--you can buy from the farmers' markets for decent prices, seasonally obviously, but there are cracks there, too. Over here, apart from the recent re-introduction of some (often none too cheap) farmers' markets, it's completely bonkers.