A member of the public made the distressing discovery on a footpath between Cranwell Avenue and Burrow Beck at 9.30am on Monday April 25.
Inside the carrier were two adult rabbits, one black and one grey, as well as a very small baby rabbit, which is thought to have been only a few days old.
The finder reported the incident to the RSPCA and their inspector Will Lamping is now investigating.
Will said: “We don’t know at this stage if the rabbits were dead when they were dumped but it is very suspicious that they were abandoned in such a way and we are keen to find out about the circumstances of this incident.
“I am keen to find the person who owned these rabbits to find out exactly what happened and to check on the welfare of any other pets they may have.
“The dirty pet carrier was red and grey with a lot of faeces inside as though the rabbits had been in the carrier for some time before they died.”
Anyone with any information about who is responsible for the incident, or who may have seen anything suspicious in the area, is asked to call the RSPCA appeals line on 0300 1234 999.
Will is also keen for local residents to check any CCTV which may help the inquiry.
Despite rabbits often being perceived as an ideal ‘starter pet’ for young children, they actually have very complex needs and are one of the most neglected pets in Britain.
It means sadly the RSPCA deals with many calls about bunnies where they have been neglected or abandoned and centres are being overwhelmed with rabbits.
Coupled with this there has also been a reduction in people coming forward to offer them new homes.
To help the RSPCA to continue its work rescuing, rehabilitating and rehoming animals in desperate need of care, you can visit their website here or call the donation line on 0300 123 8181.