Jolyon Maugham, founder of the Good Law Project, said on Twitter on Thursday morning: "Already this morning I have killed a fox with a baseball bat. How's your Boxing Day going?"
His tweet sparked outrage on social media - although he has since referred himself to the RSPCA animal charity.
Mr Maugham has since further tweeted: "Sorry to those upset by my tweet. My chickens were very distressed by the fox - both before and after I'd despatched it - and I wanted it out of the way quickly.
"I was slightly shocked by the whole tooth-and-claw experience when I tweeted and that was what I was trying to convey.
"But my tweet, one of a number about keeping chickens in urban London, should have conveyed that better."
An RSPCA spokeswoman said: "We've been made aware of this and are looking into it."
The RSPCA said on Twitter that the incident was "distressing", after Twitter users tagged the animal welfare organisation in Mr Maugham's post.
Mr Maugham claimed the fox had "got caught up in the protective netting around the chickens" and he "wasn't sure what else to do".
Government guidelines state that if a fox is caught in a trap or snare on a person's property, they must "humanely kill any fox you catch while it's in the trap or snare".
Gassing or poisoning foxes is prohibited.