We have a Bosch Accutrim like the second one on this page:
http://www.cheapmowers.com/acatalog/Bosch_Strimmers.htmlIt uses a little plastic blade rather than conventional strimmer line. The blades wear down and have to be replaced, though, just like line. But it's very effective for lighweight jobs, or working near plants that you don't want to damage.
The battery lasts a reasonable time for what we use it for. Perhaps an hour at most.
I wouldn't recommend it or any battery strimmer for all-purpose allotment use though.
And it isn't that cheap, either. You can get a Ryobi petrol strimmer at B&Q at the moment discounted for the same price, and that'll work perfectly well for all but the toughest allotment jobs.
Try this:
http://www.diy.com/ and find Ryobi Line Trimmer 25cc On offer at £67.58