Hi
No such thing as a stupid question. Only 'not' asking when you don't know something could be viewed as not being sensible :-)
Sorry, I should have made it clearer. Its Tyne and Wear Archives, Blanford Square, Newcastle ( within the Discovery Museum). They hold the workhouse admissions for Harton.
http://www.twmuseums.org.uk/tyne-and-wear-archives.html is their website.
They have an online catalogue of their holdings and also some very useful 'user guides'. This user guide details the records they have for South Shields Union Workhouse
http://www.twmuseums.org.uk/userfiles/UG22.pdfYou would need to visit the archives in person to look at the records or the archives offer a research service, but that could end up being costly (its not overpriced, but it 'can' take a long time to find what you are looking for). If you have details of dates etc, you could try asking on the look up requests board to see if if anyone is willing to do a look up when they are at the archives.
Boo