The only place I can find them in Penge directories is at 77 Anerley Road (their address in the 1901 census):-
1896 Edward Henry Scott. MRCVS, veterinary surgeon
No sign of any of your Robinsons elsewhere in this directory.
1902-11 Mrs Jane Robinson, dress maker
1912-17 Jn Thos Robinson, printer
and Mrs Jane Robinson, dress maker
1922 Mrs Jane Robinson, dress maker
and Arthur Scott-Turner. MRCS, LRCP, physician & surgeon
1923-33 Mrs Jane Robinson, dress maker
and Arthur Scott-Turner. MRCS, LRCP, physician & surgeon and medical officer, district No 1, Croydon Union
1934 Mrs Jane Robinson
1935-37 Jn T Robinson
1938-39 Jn T Robinson, printer
I don't have directories for the gap years (if, indeed, any were published then). They did not resume after Ww2.
1939 Electoral Roll, dated 15-Oct-1939:
Florence Julia Robinson
John Thomas Robinson
Minnie Beatrice Rose Shillitoe
I don't have ERs for 1945-47. 1949 has surnames Eggleton, Ashdown, Gleadle, Jeffery, & Morris
The area was redeveloped after WW2 and the house was demolished.
