"These greenouses need to be heated as well. "
They do indeed, and increasingly large scale greenhouses are being heated using heat from an anaerobic digestion plant (which would otherwise just be waste, discharged to the atmosphere). There is a 10ha greenhouse on a farm near Boston, Lincolnshire which was erected specifically to harness the waste heat from an AD plant that had been built there a few years previously (the main purpose of which is electricity generation).
And yes, it produces strawberries all the year round (around 1200 tonnes of them!)
British Sugar have a similar AD plant and an 18ha greenhouse set up near Kings Lynn, fueled by the waste from processing sugar beet - it used to produce a large proportion of the tomatoes sold in the UK, but nowadays is used for pharmaceutical crop production, which is significantly more profitable).
In both cases, the AD plant is primarily for electricity generation feeding into the grid, and that is where the money is made, so the heat is just a waste by-product, and for the greenhouses is effectively free.
"Not an issue if you like you potatoes and turnips"
Add to that: carrots, parsnips, beetroot, leeks, onions, cabbages, Brussels sprouts, cauliflowers, spinach, kale, broccoli etc.........all of which are produced all year round on UK farms - outside; in fields, with no greenhouse needed at all.