The best vegetables to grow in my polly tunnel uk?

 A polytunnel can increase the number of plants that can be successfully grown in our climate and will allow you to grow vegetables all year round, even in  northern parts of the UK. 

A polytunnel can give some insurance against the vagaries of the British weather and can also help to reduce problems with pests.  

You can grow a huge variety of things in your polytunnel. In the winter you can fill your tunnel with winter salads, winter cabbages and other brassicas, winter onions and early peas and even the very earliest of first early potatoes, that will be ready by early June. 

While the seasons are extended considerably, it’s not advised to grow any plants outside of their extended seasons. These crops are unlikely to thrive.

As it warms up in spring and into summer things like tomatoes, squash, cucumbers, summer salads and peppers of various sorts.  You can also use them to grow some fruit, strawberries, melon, 

Tomatoes do well in a poly tunnel, or maybe cucumbers / courgettes.

I have a green house and grow mainly tomatoes which don’t do great outdoors in the northern half of the U.K.

Potatoes grow outside so I wouldn’t waste your poly tunnel space. Peppers and chillis , need help in the U.K. , things like iettuce, carrots, brocolli etc grow ok outside but you can get a head start with a poly tunnel. 

Also useful for bringing in flowering plants which are tender to frost.

Potatoes aren't vegetables.

You can grow anything in one of those. From spuds to lettuce. Go for it.

U.K.

Polly tunnels are for comercial growers where you need exta protection you dont need them in summer its too hot i grow all sorts potatoes command too much area for too long carrots lettuce onions spring onions beetroot can have a few sowings set a rota the tunnel protects from frost and you can start earlier 

Figure out what the growing season is and plant those veggies that can grow in that short of time.   In Spring will you convert over to a regular garden? Cool season crops.   My guess is you would plant things like broccoli, cabbages, lettuce, green onions, radish, spinach.  Try a tomato, if you can get the setting temperature right.