strawberry plants and frost

I got three strawberry plants from the garden centre a few years ago for my son, then four, to look after and call his own. I didn't have the allotment so we dug a rectangle out of the boarder about 1m by 4m (my husband said it looked like a grave!) and we put all sorts of veg with the three strawberry plants. I don't know what variety they are but they are big plants with big fruit and they have now spread all over the patch. I'm thinking of taking some runners down the allotment as the variety I've got down there is much smaller and not as productive. One of the nice thing about the leafy variety is that the berries are hidden under the foliage. Even with netting, the birds can see the allotment ones and force a way in.