Sounds like your council's idea to scrape some more money into the Council tax kitty. Fact: Your extra garden has been rented for many years.
Has there been any increase in rent during that time, and how was it handled then?
Was your house once a council house and if so did you buy it under the "Right to buy" scheme?
Have you had no warning at all of this demand?
I cannot see why you should have to pay for legal work which you did not request. There was a a similar rumpus in our village over who cuts the grass in front of the one time council houses. The District Council handed all responsibility for what had been Council controlled housing (now including some in private ownership) to a new agency.
The new owners tried to make the flat grass cutting cost the responsibility of each and every occupant, regardless of who owned waht or indeed whether there was grass in front at all