Road between, and parallel to, Ascot and Cromer Road.

In this 1938 OS map, the north border of Mitcham can be seen along the River Graveney.

1938 OS map, courtesy of National Library of Scotland (re-use CC-BY)

From the 1910-1911 street directory:
Boscombe road, from Links road

WEST SIDE

1, Frank Andrews HOLLAND
2, Alfred NICHOLS
3, Frederick EDGSON
4, Charles John BUTLER
5, William MARSHALL
7, Charles James HANCOCK
8, Horace SPOONER
9, Thomas BLISS
10, Frederick KEMP
11, Sydney RICHTER
12, William AUSTIN
13, Robert JAQUES
14, Stanley NORTHCOTT
15, William BRAITHWAITE
16, William KNOWLES
17, Ernest James WIGGINS
18, Charles Frederick WOOFENDEN
19, George Edward MARSHALL
20, Charles Cecil GRAMMER
22, Walter John SIMMONDS, insurance superintendent
23, Richard F. LAWSON
25, Mrs TURNER
27, John Thomas WILSON
28, Samuel HONEYBALL
29, Charles George TERRY

EAST SIDE

Westerham Villas:

1, Edgar Percy NICHOLSON
2, William GUNNETT
3, Charles KEYSELL
4, William AUSTIN
5, Frank TURNER
6, Harry BUNNING
7, Gilbert D. MOON
8, Harry JONES
9, Miss BAYLIFFE
10, Thomas GRIMSHAW
11, Stephen V. LOVEGROVE
12, Charles Ernest FOWLER

26, Albert W.J. FURSE
28 (Rosaville), William HENLEY
30, George RAMPTON
32, Mrs CARRUTHERS
36, A.G. COOPER
40, Otto KRISE
42, Douglas W. CLARK
44, William MUSK
46, Walter Frederick GARDENER
48, Alfred Henry BAILEY
50, W.H. Edwards
56, Thomas Henry YOUNG