Hi Buzz,
I've recently re-visited William's baptism.
There are a couple of mistakes in your comments here about William.
In 1851 he was indeed with Rachel, (albeit named as Fredk) born about 1800, Middx, St Pancras.
However in 1861 he was a widower living with his son Archibald George, born about 1800, Middx, Bloomsbury.
Also according to the IGI his first daughter was Jean (named after Rachel's sister?) not Jane.
It is my experience that when censuses give different birthplaces, the one to put least faith in is the "default" of being born in the same place as the census was taken - in this case St Pancras.
In 1861 he specifically named Bloomsbury, not St Pancras, as his birthplace!
So I favour a birth & baptism in Bloomsbury.
I've many times previously looked on Ancestry and found nothing obvious, but very recently I came across a baptism at St Giles in the Fields, which is close to the southern edge of Bloomsbury. I think this church's records are a very new addition to Ancestry and only cover baptisms 1800 - 1812 so I was lucky to find:-
2nd May 1800 William Burrows of William & Jane
The location is OK for Bloomsbury & the date is spot on - I dont think we will find a better candidate. (Pity about the Jane connection)
I also found a sister of William, same church,
7 Apr 1803 Jane Elizabeth Burrows of William & Jane
Regards,
Brian