Hello and welcome!
I live just up the road from you near Avonbridge. Not interested in an allotment personally, as I have more then enough with trying to keep up with the garden here. They definitely used to have allotments/community garden near boghall because I used to work with a guy who was involved there.
The only other thing I am aware of is that one of the garden centres just outside Linlithgow was starting up allotments. Can't remember if it was Rouken Glen or Hopetoun House garden centre, but one of the two. Might be a little far too travel for you though.
Beth