Posted: 03/01/2015 at 18:33
I agree that trying to maintain a lawn in the type of situation you are describing would be an uphill struggle and I like some of the above suggestions. I would, however, be a bit wary of paving the whole area.
It sounds as though your back garden faces north like mine. In winter the paving at the back of our house becomes lethally slippery with algae & frost. I would, therefore, suggest considering using gravel or pea shingle over permeable membrane instead of all paving. This would be a lot cheaper and would cause fewer problems with local flooding issues as rainwater can soak through the gravel and membrane.
You can still have pots and beds or you can plant through the gravel & membrane. A bog garden or raised beds sounds like a great idea too. If you were to consider the gravel / shingle idea I suggest you go for slightly larger size stones so you and the dog don't traipse then inside all the time!
Good luck - we love to see before & after photos...