Hello Jukka,
Here is what I have found so far about Great Britain's 1935 WC games.
19 January 1935 -- CAN 4:2 GBR (0:1, 2:0, 2:1)
1. Great Britain, Carl Erhardt
2. Canada, Norm Yellowlees (Romeo Rivers, Vic Lindquist)
3. Canada, Albert Lemay (Tony Lemay, Archie Creighton)
4. Great Britain, Gerry Davey
5. Canada, Norm Yellowlees (Vic Lindquist)
6. Canada, Tony Lemay (Archie Creighton)
22 January 1935 -- GBR 1:0 FRA (1:0, 0:0, 0:0)
1. Great Britain, Bob Wyman
23 January 1935 -- GBR 4:1 AUT (0:0, 2:1, 2:0)
1. Great Britain, Gordon Dailley
2. Great Britain, Gordon H. Johnson
3. Austria, Baron Hans von Trauttenberg
4. Great Britain, Gordon Dailley
5. Great Britain, Ernie J. Ramus
26 January 1935 -- CAN 6:0 GBR (2:0, 2:0, 2:0)
1. Canada, Anthony (Tony) Lemay
2. Canada, Norm Yellowlees
3. Canada, Albert Lemay
4. Canada, Archie Creighton
5. Canada, Norman Rivers
6. Canada, Albert Lemay
And here is what I know thus far about Great Britain's 1938 WC games:
11 February 1938 -- GBR 1:0 GER (1:0, 0:0, 0:0)
1. Great Britain, Jimmy Kelly
15 February 1938 -- GBR 1:1 USA
1. United States, Art Bogue
2. Great Britain, Gerry Davey
20 February 1938 -- CAN 3:1 GBR (3:1, 0:0, 0:0)
1. Canada, Reg Chipman (Johnny Godfrey)
2. Canada, Pat McReavy (unassisted)
3. Great Britain, Gerry Davey (Alex Archer)
4. Canada, Johnny Godfrey (unassisted)
Hope this helps. I will keep looking further into other archives to see if I can find other details regarding the 1935 and 1938 Great Britain games.