The letter, from the charity's UK Director Elisa Allen says: "We at PETA – like so many devoted Doctor Who fans worldwide – are excited to see Jodie Whittaker step into the Doctor’s shoes.
"But before she begins to navigate her way through space and time, we have a request we hope you’ll consider: make the character vegan."
According to Allen's letter: "Eating dead animals simply doesn’t fit with the Doctor’s moral compass since, as Christopher Eccleston so aptly said, the show has ‘the central message of love for life in all its forms."
She goes on to describe some of the abuses suffered by animals in the industrial faming complex.
The environmental benefits of a plant-based diet are also highlighted. Allen writes: "Not only is switching to a vegan diet infinitely kinder to animals, it’s also one of the best ways to protect planet Earth, as animal agriculture is a major producer of the greenhouse-gas emissions that contribute to climate change.
"Considering all the benefits that eating vegan has for a person’s heart, it’d be doubly beneficial for the Doctor!"
Allen adds that adopting a vegan diet doesn't need to affect the variety in your diet.
She writes: "Vegan foods really have come a long way since the nut cutlets of the Sixth Doctor’s time – there are tasty options readily available to suit every appetite (even if that’s for faux-fish fingers dunked in soya custard).
"We hope the new Doctor will join us in taking a stand for animals and inspire others to switch to a healthy, Earth-friendly, life-saving diet."