The musician, who is a keen animal rights campaigner, was horrified last month (Jul15) when it emerged the beloved beast had been shot dead in Zimbabwe after it was allegedly lured out of a protected zone.
The heartbreaking tale caused outrage around the world, but May is convinced "some good" can come from the horror if supporters push for a 'Cecil's Law' to ban the importation of "trophies" hunters take from their protected prey, such as hides, body parts, or ivory.
He tells the BBC, "For once people got up and said we don't accept that this is the way people should carry on... This animal was caused to suffer and it's the tip of the iceberg. There are animals everywhere being abused by people at the moment and this opened it up. People are now asking the question.
"We may, thanks to this, have a Cecil's Law. We should have a Cecil's Law which forbids the import of any trophies from any country and we should stop trophy hunting in this country too."