Below is a copy of the answer I received this morning from the archivist at the Portman Estate which owns this and surrounding properties. Funnell was the man who had a business on the ground floor and seems to have leased the building later on.
Thank you for your enquiry. The estate’s records show only the names of lessees, not occupiers or sub-tenants so I regret we cannot be of direct help to you on this. In 1919 13 New Quebec Street was still subject to a 56 year lease granted in 1870 to Edward S Jones and assigned in 1883 to another member of his family. A new lease was issued in 1928 to a John Funnell.
If you have not already contacted them you would be able to find more details about the occupiers of this property from the City of Westminster Archives Centre, a collection which is fully open to the public. Their website is
www.westminster.gov.uk/archives The best sources to try would probably be street directories, the St Marylebone rate books and possibly the electoral registers for 1919, all of which you would find there.