According to 'Handsaw Makers of Britain' by Schaffer and McConnell, there is no record of a Cope making saws in London or anywhere else. However, there are two Coopers and six Copleys listed as London makers.
Frederick Cooper jr., 28 Austin St Shoreditch, 1899-1910
Mrs Sarah Ann Cooper (succeeding Frederick Cooper jr.), 29 Austin St Bethnal Green, 1914-1915.
Albert Copley, 90 & 92 Oakley St Lambeth, 1882-1910
Alexander Copley, 668 Commercial Road, 1910
John Copley, 43 St George St, 1852
John Copley, 28 North Woolwich Road, Canning Town E, 1874
John Copley, 28 Victoria Dock Road, 1882
John Copley Sr, 668 Commercial Road East, 1891-1899
Not sure if that might help.