Hi
Ancestry lists what parishes are online under the geographical headings of the modern London boroughs. Rotherhithe and Horsleydown are Southwark. St Botolph without Aldgate (1754-1921 online) is the City of London. The lists are in 'Browse the collection' on the right in the marriage section or baptisms, and burials.
Having children baptised isn't evidence that the family were regular churchgoers or that it makes it 'inconceivable' a marriage didn't take place. There may have been an impediment to the marriage or they simply chose to live together or married somewhere else like a parish in Westminster (Westminster Archives parishes other than Bishops Transcripts are not online though Findmypast does have the West Middlesex Family History Society marriage index) or married later. This is a period before stricter Victorian morality which was far more to do with inheritance and the middle classes.
Should you also be looking for the marriage in Robertson - Richard's alias which might be his real surname, he seems to move between both?
31st August 1810 St Mary, Whitechapel, Middlesex
Louisa Hannah Robertson parents Richard and Mary Hannah, Rose Mary Lane
same church
8th August 1810 born 6th August 1807
Mary Elizabeth Robinson parents Richard and Mary, Rosemary Lane
possible for Richard's baptism
10th August 1809 St Andrew Undershaft, London born 29th December
1808 Richard Robinson parents Richard and Mary
see
http://www.historyaustralia.org.au/twconvic/tiki-view_forum_thread.php?comments_parentId=56&topics_offset=6&topics_sort_mode=lastPost_desc&forumId=1for the names of the four children born in England
and
http://boards.ancestry.co.uk/thread.aspx?o=0&m=6220.1.2.1.2&p=localities.oceania.australia.nsw.generalfor the possibility the mother's name was Mary Hannah
It is always best to start a new topic when you have a question rather than place it on someone else's topic. That way more Rootschatters will see it and hopefully help and you aren't diverting the original topic. I will split off your topic and start it as a new one on the London board.
Regards
Valda
co-moderator London and Middlesex