Cox, who has been described as "comedy gold" in online show reviews, said: "It came out better than I thought it was going to".
Show judge, the tycoon Lord Sugar tweeted to his 2.5m followers: "Do you think the garden centre man is a relative of Bill Oddie? The garden centre man is a real character."
In the programme Cox was asked for a discount on an olive tree by Lord Sugar’s 17-year old protégée David Odihambo, but he refused, saying: "Why should I give you a discount"? "Do I ask my staff for a discount on their wages?"
"We are desperate", said Odhiambo. "If you’re desperate you would pay anything", replied Cox.
Fellow contestant Lucy Beauvallet noticed a sign saying "10 per cent of houseplants" and asked if an olive tree could be a houseplant. Cox gave her 10 per cent off.
Cox, who has owned the centre for 25 years said it was a bit of fun. "Quite a few customers have mentioned it and friends [have] given me some grief so we have a sign on the gate saying 'no discount' now.
"If I was to give a discount I’d have to give staff a discount off their wages because giving discounts disrupts profitability and buggers up costs. No-one else has asked for discount. They haven’t dared, though some of my friends do it as a joke to wind me up."
He added: "It was nice to be on BBC1 and not the Discovery Channel. The BBC get you to sign a form saying will you give up your rights for a penny. But I wrote on it that I didn’t get my penny."
However not everyone was amused by the episode. Joel Beckman, managing director at London's N1 and W6 Garden Centres said he was "horrified" by the scene: "Even if that's what one was thinking when serving people in this scenario, we don’t think it's acceptable to talk to a customer like that. I am sure lots of garden centres get asked for discounts - we often do of course - but there are polite ways of declining."