But the council says it is looking at the possibility of a grace period for the farmer and is offering him support to find a new home.
Mr Garmston, 57, from Myddle, lives in the smallholding that firstly his father, then himself rented from the council, all his life.
In March his 15 year tenancy comes to an end and he has been told he will have to leave the property.
His plight, highlighted by the Shropshire Street Cats charity, has brought hundreds of messages of sympathy for Mr Garmston and offers to rehome the cats.
Shropshire Council, director of place and enterprise, Mr Mark Barrow, said: "Mr Garmston has been a valued tenant of a Shropshire Council-owned smallholding for many years, most recently under a 15-year Farm Business Tenancy which reaches the end of its term in late March.
“We have been in discussions with Mr Garmston about this since January 2020 and offered him the opportunity to buy the property in which he lives.
"During the past 13 months Mr Garmston has not requested an extension to his tenancy nor have his professional representatives.
“Given the circumstances we are, however, talking with Mr Garmston about the possibility of a grace period at the end of his lease.
"Our housing team are also offering Mr Garmston support to help him find a new home at what we fully appreciate is a difficult time for him.
"This would also give him more time to rehome any of his animals.
“Mr Garmston’s situation reflects significant changes in agriculture, where farming on such a small scale has become increasingly difficult, particularly for livestock and dairy farmers.
“At the same time, we have a duty to our council taxpayers to seek to secure the best value possible from our assets, which includes such smallholdings.
“As many will understand, these smallholdings require ongoing maintenance and there is obviously a cost associated with this.
"The eventual sale of this smallholding, and others that the council owns, will enable the council to build many more homes for people who need them.”
In 2005 the former Shropshire County Council, as the forerunner authority to Shropshire Council, took a decision to retain the remaining smallholding estate rather than sell then en bloc, but allow the individual smallholdings to be sold as they became vacant or were sold to the existing tenants.