The Donegall Square West branch of Caffe Nero was closed yesterday after the story broke.
The footage was filmed by a couple who spotted the rodents while returning from a night out.
While Caffe Nero said its infestation was an isolated case, Mr Kennedy, from Belfast-based Pestokill, said the number of rats in the city is increasing.
“For example, if you had a male and female rat on January 1 and they have enough food and water and shelter, those two rats could breed to the point where there are 2,000 by the end of that December,” he said.
“We would have three to five callouts per week in the Belfast area for commercial pest-related problems. It will be all business premises, which would include restaurants, golf clubs, train stations — it could be anything commercial.”
He said rats were a growing health menace — but humans had to take a big share of the blame.
“They are definitely on the increase and it will be due to our habits as residents of cities,” he said.
“Where there is man there will always be rats. If we are providing them with plentiful supplies of food, they are going to breed and expand in terms of the amount of them.”
Mr Kennedy said everybody had a responsibility towards preventing the rise in numbers.
He said: “It’s just our own fault and the numbers will keep increasing.”
After the rat footage was brought to the attention of Caffe Nero by the Belfast Telegraph, it began an investigation straight away.
The affected store was closed yesterday morning. Caffe Nero said it believed the source of the problem to be a “disused building adjacent to our store”.
A spokeswoman said: “Following this isolated incident, we have closed the affected store and launched a full and urgent investigation.”
A Belfast City Council spokesman said: “Following reports of a specific problem with rats at Caffe Nero environmental health officers have been out to ensure the premises are closed and offer advice as to how the problem should best be tackled. The council were also investigating the integrity of the external drainage infrastructure in the area and were liaising with the management of the Scottish Provident Building, who carried out immediate maintenance to the drainage.”