Where was Woolwich in England situated in 1819?

Woolwich has always been in the same place. Woolwich  is a district in southeast London, England, within the Royal Borough of Greenwich. It has been part of the London metropolitan area since the 19th century. Throughout the 17th, 18th, 19th and most of the 20th century, Woolwich was an important naval, military and industrial town. Prison Hulks ( ships that were incapable of sailing) were used to house prisoners sometimes for months then transfered onto ships for sailing...so your ancestor was likely held on one of the Hulks on the river Thames at Woolwich London, to transported to Austrialia...

https://convictrecords.com.au/

https://guides.sl.nsw.gov.au/c.php?g=671838&p=4729...

https://www.royal-arsenal-history.com/prison-hulks...

Same place as it is now.  If you're asking what county it's in, there was no county of London at the time so it was in Kent.

The whole of what is now Greater London used to be split between Middlesex, Surrey, Essex and Kent.  In 1889, it was decided it would make more sense to have a proper city government and the county of London was created.  Woolwich was the easternmost part of that.  London expanded further and in 1965, the county was expanded again to make the much bigger Greater London, and Woolwich is now definitely inside that, in the Royal Borough of Greenwich.

So it's a bit of an odd question because in 1819, there was nothing officially called London apart from the very small City of London.  Obviously the city existed but it didn't have any city government.  So for any records of Woolwich back then you have to look under Kent.

The site was occupied in ancient times; there is evidence of a Roman cemetery, and the place-name Uuluuich, from which Woolwich is derived, appears in legal records from 918 CE. Early in the 16th century, Woolwich rose to prominence as a dockyard and naval station. In 1512–13 Henry VIII established a royal dockyard there to build the Henry Grâce à Dieu, or Great Harry, the flagship of his new navy. (In 1553 the ship was destroyed in a fire at the port.) Ships were built there for Sir Francis Drake and Sir Walter Raleigh. Woolwich remained the chief dockyard of the British navy until the introduction of ironclad ships; the dockyard was closed in 1869.

South east London close to the border with Kent. Original site of the Royal Arsenal which is where Arsenal FC got their name from although they moved to north London in 1913.

It would have been officially part of Kent at that time.

It was in Kent, the boundary with London was upstream at Rotherhithe. 

It officially became part of London in 1889, but had been (informally)

considered part of it by the mid 19th century.

somewhere around london