I saw the begging reference as well. I can't make out any address so wonder if it was some sort of communal housing (nice way of saying work-house)?
On the 1841 Mary is shown as being born in Ireland, on 1851 she is shown as being born in London. All the other details seem to fit though.....
I suppose that it is entirely plausible that she could have had 2 children without John (the scandal!) but there are all sorts of possibilities between around 1848-50 that could explain his absence (death, jail, war, divorce?) The only John Bourkes that I can find dying around the dates are in Chichester and Manchester