Belated thanks, billy 
This scene-stealing animal is found by Marla Landi in the pre-credit sequence of
HG Wells’ Invisible Man -
The White Rabbit (1959):
Available on You Tube, Camelot Broadcasting and the
Internet Archive. I wish they'd been around in the 1950s ...
The White Rat in this
Gideon’s Way episode, from 1964, is the nickname of albino villain Ray McAnally as well as his pet:

With Virginia Maskell as Ray's misguided girlfriend.
Callan (Edward Woodward), who has just saved the life of his boss, finds this cat in
Red Knight, White Knight (1969):

"I think he's got nine lives, mate. He's gonna need 'em all."
Judy Cornwell, one of
Dr. Hoffman’s Children, is also seen with a fluffy white cat in (the return of)
Van Der Valk (1991):