Research

Some places I have found on my hunt for the year that they introduced the modern KX100 phone boxes into the UK (there's a reason for my search I promise I'm just not going to share):

telephones uk: a pictorial history of telephones in the UK - I think they cover most phones not just the kiosk variety but I was only looking for the change over date so I didn't stay very long.

redphonebox.info A comprehencive history of the British Phone Box.

In case you're interested the KX100 was introduced in 1985 and the more familiar KXplus (which included a red phone box banner round the top and a domed red roof) was introduced in the late 90's - the latter are I think the one's I was thinking about but if anyone could give me a date when they started introducing them that would be great.