Hi Diddy
The 1871 Jarrow family do indeed look to be Mary Ann and Elizabeth living as wife and child with Thomas Purvis (RG10 5040 70 p33 - It's best to always give this citation in case the entry has been indexed under the wrong name). In addition you can find young William Charlton, the son, living with his Grandparents in Percy (RG10 5115 36 p2).
With Thomas Charlton, the father, living until Sep 1871 there is clearly some irregularity in the census claim that Thomas was married - Mary Ann was probably married but to William not Thomas. Thomas is recorded as born in Eyemouth, Berwickshire so he was Scottish. At this time the Scottish law on marriage differed from English law in that the relationship did not need to be registered to be established it was sufficient that the couple should set up house together and jointly acknowledge parentage of any children. So Thomas may not have been aware of this difference between English and Scottish law and probably considered himself married because he was living with and having children by Mary Ann.
Of course if you should discover a registered English marriage between the couple before September 1871 then it would almost certainly have been a bigamous marriage.
It is probably not relevant in this case since I imagine that Thomas was not a wealthy man but had he been there might have been all sorts of complications with his estate when he died - see Wilkie Collins's novel "No name".
All the best
Gobbo
Whoops in the original post I wrote "William" instead of "Thomas" at the start of the second paragraph and hence confused Diddy as well as myself. Sorry!