Here goes, first time post!
We had a problem with similarities to your own, Ladygrey. If I relate how we dealt with that - not perfectedly, but what in a smallholder's life ever is - it may be of use and interest to you and, possibly, others.
Most of our pasture is between two arms of the river that cross our land. We have a field shelter serving that and in past years our ewes lambed in the field - fortunately consecutively, rather than concurrently - and we used it to provide shelter and bonding space for the days after each birth. However of recent years, with ever wetter autumns, winters and springs, we have suffered an increased risk of this land flooding and so in 2012 we fenced in a large part of our back garden, to provide winter quarters above river level, and the adjacent lean to shed served for lambing and overnight shelter, the ewes and lambs sharing, of necessity, with geese, ducks and chickens. However with even yet more rain this autumn and winter, it's become increasingly more difficult to keep that dry (due to water permeation through the walls, due to the abnormally high water table) and so with lambing in prospect we were forced to think again.
Immediately adjacent to our kitchen door is a wood shed. Because it's raised about 20 cm above the surrounding land and thus generally doesn't flood or suffer water penetration (the leaking roof is on my summer works' agenda), we decided to use this for lambing and devised a temporary conversion that would allow it to revert to its original purpose at times other than when needed for lambing and post lambing accomodation for our ewes and their lambs. It measures 3.5 m by 4.5 m, with a former window opening on the north elevation and was entirely open on the east elevation. We closed up the former window opening with a pallet, timber battens, left over waterproof roofing membrane and an old blanket. The eastern elevation was partially closed by nailing old doors, planks and suchlike across one half and we partially enclosed the other half using pallets - one fixed and one hinged as an entrance door - covered, again, with roofing membrane and old blankets (stapled in place).
We were fortunate to be able to source, free of charge, about a dozen substantial wooden pallets from our feed merchant. In addition to the uses already mentioned, these we used to make three lambing pens, about 1.2 m by 1.2 m, inside the wood shed. Because we didn't want them to be permanent and we wanted to be able to revert, subsequently, to the original open plan interior, we didn't screw or bolt them to the floor or walls but braced them, with old wooden battens, so that the ewes could not push them out of place, and held them in place with concrete blocks and/or fixed them to whatever pre-existed and was suitable. The pallets are secured together with heavy duty bailer twine and the same is used as 'hinges'' and 'locks' to the doors of each pen.
It seems that this rather ramshackle approach has served its purpose. Our three ewes and their five lambs seem to like the pens and the shed so much that they complain bitterly when we drive them out into the yard that was our back garden! But the important thing is that the animals are warm, dry, content and seem to be thriving. And when - hopefully - we turn them out into the riverside pasture next month, we should be able to dismantle the pens, number the parts and stack them in the corner of the shed until spring 2014.
I will try to attach some pictures of that which I've described (although frequently I seem to make a mess of this on my first attempt on a new forum). I hope that all of this may be of some help