According to a statement from Sevenoaks District Council, the authority issued Bhupinderjeet and Narinder Kullar with two planning enforcement notices in December 2016.
The notices required the couple to cease operation of The Convent of Mercy hostel and remove a wooden shed that had been built without planning permission.
Mr and Mrs Kullar failed to comply with the notices, the authority said, and continued to operate the hostel until March 2018, when the council obtained a closure order.
The council statement described the property as a "notorious illegal hostel" and said it had been the cause of anti-social behaviour and safety concerns since 2014.
According to the council, Kent Police attended the premises on several occasions. The local authority issued a community protection warning in January 2016 and a community protection notice in October the same year in relation to anti-social behaviour and litter.
In August this year, Mustafa Kemal Mustafa, who ran the hostel, was fined £15,000 for failing to comply with a planning enforcement notice, the council said.
And earlier this month, the Kullars were hit with a £4,000 fine and told to pay £10,000 in costs after a four day trial at Woolwich Crown Court.
Alison Salter, planning team manager at Sevenoaks District Council, said: "Mr and Mrs Kullar did not comply with our planning enforcement notices for a number of years. Only by taking action in the courts was it possible to close this unlawful hostel.
"The building was not fit to be a hostel and there were numerous reports of anti-social behaviour associated with its tenants. The £14,000 fine sends a clear message that we will not tolerate people who ride roughshod over the law."
Earlier this month, a Nottinghamshire woman who unlawfully built her own flood defences in a high risk flood zone was ordered to pay almost £1,400 by magistrates.
Last month, Planning reported that Newark and Sherwood District Council won an enforcement case against a man who demolished a 19th century barn in a conservation area without planning permission.
Also last month, Planning reported that a landlord who illegally converted her west London home into a house in multiple occupation (HMO) has been ordered to pay more than £400,000 under the Proceeds of Crime Act (POCA).