Dickson-Wright, from Midlothian, Scotland, and Sir Mark Prescott, of Newmarket, Suffolk, admitted attending two hare coursing events in north Yorkshire in March 2007.
Neither defendant appeared in person at Scarborough Magistrates' Court for the private prosecution, which was brought by the International Fund for Animal Welfare (IFAW).
The court heard that Dickson-Wright, who found fame in the television cookery series Two Fat Ladies, and Prescott admitted attending one hare-coursing event on March 2 2007 near Nunnington, and another the following day near Amotherby.
Hare-coursing, in which hares are pursued by greyhounds, was banned by the Hunting Act 2004.
The court heard the events were organised by the Yorkshire Greyhound Field Trialling Club (YGFTC) and saw 46 trials, each involving two dogs chasing hares, over the two days.
John Cooper, prosecuting for the IFAW, described the events as "significant and concerted".
He said: "During the course of both these events, the dogs were muzzled but that does not stop the damage and harm to the wildlife they chase and harry simply because they are muzzled.
"It in no way ameliorates the suffering that the hare would feel from the chase and, indeed, simply because the dog has a muzzle around its mouth may mean it can't bite any quarry it might catch but does not mean it cannot injure that animal.
"It does not ameliorate the cruelty."
Mr Cooper continued: "What we have is a sophisticated, large and well-attended gathering which was consciously trying, by the methods it used - muzzling and the use of the gun in particular - to blur the distinction and avoid prosecution under the Hunting Act."
Last month, three-times champion jumps trainer Peter Easterby and Major John Shaw were found guilty of permitting land to be used for hare coursing at the same events.
The pair were also convicted of attending the event.
Both denied the charges and claimed they were not aware that what was taking place on their land was illegal.
In mitigation for Prescott, Stephen Welford said his client was invited by the YGFTC, which believed it was running a legal and "above-board" event.
He said the club sought advice from a firm of solicitors and leading counsel and received insurance.
A police officer attended the event on the first day but left a short time later.
"The events were not hidden," Mr Welford said.
Barry Warburton, for Dickson-Wright, said his client had also been invited and thought the event was legal.
Neither defendant had any previous convictions.
Both defendants received an absolute discharge and no costs were awarded against them.
But District Judge Kristina Harrison said any future offenders would be dealt with more seriously.
She said: "I found the previous defendants guilty of hare-coursing. I don't want anybody to be under any illusion that I was doing anything other than saying what they did was wrong and it was unlawful.
"What I had sympathy with was there were complexities within the Hunting Act which made the administration of it a little difficult at first.
"I hope that this case makes it perfectly clear to anybody who wants to undertake this type of event: forget about what an expert says is hare-coursing, forget about what hare-coursing was before.
"If what's happening fits within the definition set down by Parliament within the Hunting Act, it's hare-coursing. It's unlawful, people will be prosecuted and will be dealt with severely."
District Judge Harrison described the case as "odd" and said she believed the YGFTC tried to stay within the law when organising the event.
She said she believed the event would have been stopped if anyone had told the organisers it was illegal and said the two defendants in this case had "held their hands up" once they were told what they had done was wrong.
The judge continued: "I impose for both of these people an absolute discharge and I do not award costs in all of the circumstances.
"The judgment is not intended to condone hare-coursing, or say that people from this point on can continue hare-coursing and receive an absolute discharge."
She said anyone convicted of such an offence in the future would be "dealt with most strenuously".
Speaking after the case, Tania McCrea-Steele, campaigns and prosecutions officer for the IFAW, said: "These guilty pleas send out a strong message to anyone considering chasing hares with dogs that they will be prosecuted.
"It will also act as a deterrent that anyone engaging in this behaviour will be dealt with most seriously."
