The RSPCA say they're at crisis point because of a rise in the number of animals being abandoned.
The animal charity say 40,000 pets were abandoned last year, compared to just 25,000 five years ago.
It thinks families struggling with money problems are leaving their pets because they can't afford to look after them.
Charities that run rescue centres say they are getting full and not enough people are coming forward to adopt.
The cost of caring for abandoned animals is also going up. It costs £15 a day to care for a dog and £9.40 for a cat.
Because some animals are unwell when they come to rescue centres, it can take a long time to look after them and make sure they're well enough to be rehomed.
The RSPCA say they might be forced to turn away vulnerable animals in the future because of the crisis.