When we're first introduced to Jenny and Sandy "He may be your best friend, Sandy, but he's my best brother!...."
She's walking what appears to be a West Highland White Terrier (aka "Westie"). Later on in the film, when she hears Eric refuses to run on Sunday, she appears to be washing the dog, who'd rather be anywhere but the tub! May be the quintessential Scottish dog besides the Scottie.
I'm partial to Westies, as I have one pure Westie, and two Westie mixes (the other mix is Cairn terrier and chihuahua). They're all females and we have a ball together - they provide the best canine companionship you can imagine!!! And yeah, they don't like baths either.
I remembered her washing the dog -- great scene -- another brilliant touch either by Colin Welland or by Hugh Hudson! That was going to be one on my list.
I had forgotten that she was walking him in the beginning though! Good catch! .