I'm guessing you've alrady Googled Shadwell.
GENUKI has information on Shadwell and the whereabouts of it's records at: http://homepages.gold.ac.uk/genuki/MDX/ShadwellStPauls/index.html
Wikipedia comes up with:
'Shadwell is an inner-city district situated within the London Borough of Tower Hamlets located on the north bank of the Thames between Wapping to the south and Limehouse to the east. It is located 3 miles (4.8 km) east of Charing Cross and forms part of the East End of London" And these churches:
"St. Paul's Shadwell with St. James Ratcliffe, is traditionally known as the Church of Sea Captains. In 1656 the church was established as a Chapel of Ease, from St Dunstan's, at Stepney. In 1669, it was rebuilt as the Parish Church of Shadwell, and it was the last of five parish churches rebuilt after the Restoration. In 1820, it was again rebuilt as a 'Waterloo church'.
The "Shadwell near Smithfield, London" came from the New South Wales death certificate of a convict in 1860. The information was from his colony born son who had no education. My premise was that he got the information diectly from his father himself.
However, it is all open to interpretation I guess. Some of it is obviously error - but which bit?
I'm not sure whether to chase the Shadwell or the Smithfield now.
I know London is correct, as he was sentenced at the Old Bailey .
Rosie