They may have worked for a contractor, a lot of this kind of 'piece work' was contracted out. so even if you were to find out which companies were in the area, the family's names may not appear in the books. Do any of the documents for the family list the father as a master tailor? If so, he may have been apprenticed and been a member of the Tailors Copmpany. I believe the records are held at the London Metropolitan Archives, you could email them for further information http://www.cityoflondon.gov.uk/lma