Thanks for the offer Di, accepted gratefully, I was at Kew yesterday and managed to get a look at the censuses: Nothing for 1851 but though they are not shown in chronological order I think this makes the most sense (At least to me!)
1871 Cambridge City St. Clements Parish, Trinity Ward
John Moule Father widower 68 Maltster b Chesterton
Lydia Taylor Head Married 45 Porter's wife
William Taylor Son U/M 15 Telegraph messenger
Robert Taylor Son U/M 12 Scholar
1861 78 Fitzroy St. Cambridge
John Moule Head Married 58 Maltster b Chesterton
Susannah Moule Wife 55 b Cambridge
1841 Back Lane Cottenham
John Moule N/S? 40 ??
1841 4 Russell St. Cambridge
Joseph Moule 70 Labourer Yes
Susannah Moule 35 Yes
1871 7 Wray's Almshouses
Joseph Moule Widower 86 Builder b Cambridge
1841 Green St. St. Michael's Cambridge
Joseph Moule 45 Carpenter b Cambridge*
Ann Moule 45
5 children
* Added detail for 1841
From these extracts I believe 1) We have two Josephs one bc1785, the other 1796 2) From the 1841 census it seems reasonable that the elder Joseph was living with his son John who happened to be away in Cottenham on census night, and John's wife Susannah.
Hope this makes sense.
ssell St. Cambridge
Joseph Moule 70