Founder Wong Wai-yin said: "Normally these owners are rushing to leave Hong Kong within a month."
She said pets often have emotional issues because of a change in environment.
"Older dogs are generally more stubborn. They are so used to the lifestyle at home it's difficult to adjust."
"We can only say the owners are irresponsible," she said.
Wong said only 2 to 3 percent of owners change their minds.
Some choose to bring their furry friends over.
Pet immigration agencies said the number of inquiries per month has surged 50 percent.
A woman, Yau, is moving to the United Kingdom in May.
She is taking her Pomeranian, Cally, with her.
"I truly think of her as a family member. I do not think any parents would abandon their children. You would leave for the children, but you would not give them up and leave on your own," she said.
As Cally is quite old, aged 13, she suffers from tumors in the spleen, inflammation of the gallbladder and a collapsing trachea.
"The vet said do not think about using cargo shipping as it is dangerous, for it would not be taken care of by anyone. So I have started to look for information about private jets," she said.
Pet Holidays consultant Fanny Liang said such moves are pricey. "Shipping may cost from HK$80,000 to HK$90,000. The cost for a jet is HK$208,000, but that includes dog and owner."
So far, more than 35,000 British National (Overseas) passport holders have applied for the UK scheme that grants a five-year residence permit, with a pathway to citizenship.
A small number of "unusual infections" have been identified in patients at the Royal Aberdeen Children's Hospital.