Green Manure

Can anyone tell me if it is worth growing a green manure on the veg plot over winter.  We generally give the plot a dig over and then cover with black polythene to keep the weeds down and warmth in but are wondering whether it might be beneficial to try a green manure this year.  A few questions, are germination rates fairly good, is the crop easy to deal with when it has done it's work and does it break down easily when it has been dug in and also would it be possible to use a tiller to break it down/turn it in?  Any replies would be gratefully received. Thanks.