Leeks, carrots and swedes have been particularly difficult to harvest in the extreme weather conditions.
Mervyn Casey of Willow Farm in New York, Lincolnshire — one of the country's largest leek growers — said a lot of supermarkets had been relying on Dutch supplies as he struggles to lift leeks out of the ground.
"The Dutch traditionally store leeks at this time of year, so three-quarters or more of the sales at the moment are coming from Holland. But I expect they will run out sooner or later," he said.
"It's very frustrating and a double whammy — there's a good demand because it's cold but we are having trouble getting them out of the ground," added Casey.
"The ground has not frozen too badly — the problem is the skins are frozen. We cannot get the outer skins off.
"The varieties we have available have not been bred for winter hardiness. It's not a characteristic [the breeders] have been looking for. Ten years ago we had varieties that would withstand this sort of weather easily."
The Really Welsh Company in Flintshire said it continued to fulfill its orders for more than 30 tonnes of leeks during last week's snow, with 35 per cent of the produce staying in Wales and the remainder distributed throughout the UK.
Mark Goodman, site general manager for Nottinghamshire-based Sherwood Produce, which grows root vegetable crops, agreed that picking conditions had been "very difficult".
He said: "Getting carrots out of the ground has been the problem because they've been covered in two or three inches of snow.
"At the moment, we are managing to fully supply. We've just had to extend our working days a little bit. Fortunately, customers are understanding and appreciate the conditions in which we have been working."
British Carrot Growers Association chairman and managing director of Midlands-based Freshgro Martin Evans said although carrot fields are protected by their layer of straw there will still be some significant crop losses.
"The extent has yet to be evaluated. Until it thaws we will not know the full impact of the damage. I anticipate that there may be some significant damage. We are worried but we are all in the same boat."
He added that one of the biggest problems had been the situation on the roads. "Some depots were not available to us. It takes a lot of good will from everyone to keep trade moving," he said.
Brassica Growers Association vice-chairman and East of Scotland Growers representative Alistair Ewan said some growers north of the border had seen up to 10 inches of snow, with swede crops being one of the most difficult vegetables to lift.
See the Horticulture Week picture gallery for winter scenes from across the country.