Hello Julie,
Thanks for looking. The Greenwich hospital one would fit. Sarah was born 16 Apr 1783 so William could be about 10 years older. Their marriage also has Greenwich:
London, England, Marriages and Banns, 1754-1921
Name: William Swalling
Spouse Name: Sarah Bachelor Newbery
Record Type: Marriage
Event Date: 13 May 1804
Parish: St Alphege, Greenwich
County: Middlesex
Borough: Greenwich
Page 278
No 2788
William Swalling of this Parish Bachelor and
Sarah Bachelor Newbery Spinster of the same
were married in this Church by Banns
this Thirteenth Day of May 1804
By me J P George Curate
Both signed
Witnesses: John Newbery, Sarah Porter ?
Deaths Dec 1847
Swalling Sarah Batchelor Greenwich 5 185
London, England, Deaths and Burials, 1813-1980
Name: Sarah Bachelor Swalling
Record Type: Burial
Event Date: 13 Dec 1847
Age: 63
Estimated birth year: abt 1784
Parish: Saint Alfege
Borough: Greenwich
County: Middlesex