Birth/baptisms source IGI for William Burrows c 1800
Nothing shown specifically for St.Pancras or Bloomsbury but St Mary Marylebone is a good second choice.
Two possible entries, all baptised at St. Mary St Marylebone.
Parents
James & Elizabeth Burrows
Children
William Burrows
born 26th May 1799
bapt. 21st July 1799
Eliza Burrows
born 13th Sept. 1799
bapt 29th July 1800
James
born 16th May 1803
bapt 24th July 1803
The birth date for Eliza looks a little suspect when you look at the birth date for William, the original PR entry needs to be checked, they are all shown as children of James & Elizabeth.
Two possible marriages for James & Elizbth.
James Burrows = Elizabeth Nixey
9th Jan 1791 St Anns Soho Westminster
James Burrows = Elizabeth Smith Kerfoot
31st Nov 1794 St Leonards Shoreditch
Parents
William & Ann Burrows
children
Harriet
born 26th Apr.1800
bapt. 25th May 1800
William
born 11th Jan 1801
bapt 11th Feb 1801
Esther
born 13th Apr. 1805
bapt 12th May 1805
No marriage found for William & Ann in the London area.
Hope this helps
Meliora