He said the MP was an 'important voice on animal welfare in the Conservative Party'.
Mr Pritchard said: "As Secretary of the Parliamentary Conservation and Wildlife Group, Brian and I regularly meet to discuss animal welfare matters.
"Whilst we don't agree on everything, we do agree that the Government needs to do far more to address animal welfare matters, for example ending primates being sold as pets."
The guitarist was meeting members of parliament to discuss the fight against the badger cull, something he has used his fame to speak out about in recent years.
In 2010, he set up Save Me, a not-for-profit organisation that speaks out against cruelty to animals, including issues such as the badger cull and fox hunting.
Last year May said he was delighted with the government's decision to delay the badger cull, but has continued his support for the cull to be cancelled altogether.
He created an e-petition called Stop The Badger Cull, which currently has more than 160,000 signatures.
Taking to his Twitter page on Wednesday, before his meeting with Mr Prit-chard, May vented his frustration at the badger cull.
He wrote: "Condemnation from the scientific community, the Govt is going ahead with the badger cull this Summer . . . Yes, in spite of everything, you should all be clear that the government, hand in hand with the NFU (National Farmers Union), is going ahead with the badger massacre."