The final UK processing address for pre-paid Kodachrome films was Kodak Processing Companies Ltd 29 Deer Park Road London, SW19 3UG, which closed in 2006 when 120 processing finished. (This seems to be the same address used by Agfa for their pre-paid reversal films way back in the 1960's/70's, though later, (when their films changed to E6) they used (independent?) labs in Bury and Coventry).
Just been wasting-a-few-minutes with Google maps of Deer Park Road, and the "street-view" shows a largish fairly-modern (1970's or early 80's) building on a busy industrial estate. The only indication of any connection with Kodak is an old banner "Overnight film processing" (and "Kodak-Yellow" painted railings).
At the time of the picture (June 2008) the building looks in good order but is empty and "To Let", while the weeds in the car yard look consistent with it being unused for a year or so. So no moth-balled K-labs to be found there now, I guess.