The register entry for William's death in 1821 indicated that his age was 70 years. I found only two baptisms that fitted this exactly and one of these was for a baptism at St Mary Lambeth which is where his children with Harriot were baptised so I have assumed this to be the correct baptism, well aware that the age 70 may not be accurate or that there may be other baptisms that I haven't found.

The entry for his marriage to Harriot states that at the time he was a widower. There are several earlier London marriages of a William Burrows at the right time but the one that jumped out was a marriage to Dorothy Roberts in 1780 at St Mary Lambeth. William and Dorothy had (at least) four children, the last of whom was buried 9 days before the burial of Dorothy (at St Mary Lambeth). Again I cannot be sure that I have the correct details but the Lambeth theme is very convincing!

Dorothy was a minor on marriage. I have assumed the baptism in 1760 at St Mary Lambeth is the correct choice although there was another at Rotherhithe the next year which also meets the search criteria.