Sorry to hear these problems but the silver lining is your inability to get on with digging. Yes, do just spread some reasonably decomposed manure or compost on top. You may not need to cover with polythene unless weeds are rampant and your mulch of organic matter is insufficient to thoroughly cover them, with no light available to their leaves. You should be able to plant as usual in spring and even sow seeds direct, especially if the organic matter has been made soft and crumbly by some frost.
Not sure about your second plot… but do remember this weather has been quite exceptional and this time next year we may be worrying about water shortage as was the case only nine months ago.