If I got a hold of a strawberry plant (Is that what their?) that's already been growing somewhere else and is producing good strawberries could I then plant it in the garden and will it continue to grow and create strawberries?
Yes... Sort of. The first year will probably still be really crap, unfortunately, because it'll spend most of its nutrients on expanding and repairing its root structure after the move, rather than on making excellent strawberries.
Raspberries also grow well in the British climate but they do take a while to take, too.
Root veg - spuds, carrots, parsnips, turnips, swedes - are just about your best bet for "ease of gardening". You can also successfully grow stuff like spring onions, leeks, rhubarb, most varieties of lettuce, rocket, courgettes and all manner of beans and peas, all of which grow fast and are relatively low-maintenance.