One Labour MP said the scaled-back events represented "one rule for the Conservatives and their mates, another for everybody else."
Labour's deputy leader took on the prime minster at PMQs on Wednesday.
Exclusive: Cabinet ministers were sent an agenda item titled "Exemption: hunting and shooting".
More than 80 meets are believed to be taking place across the course of the day
Investigators are probing whether a nearby pack of hunting dogs had anything to do with the fatal attack on Elisa Pilarski.
Thomas Alexander shot a buck while hunting in the Ozard Mountains.
Tess Talley faced backlash in 2018 when a photo of her posing, smiling and with gun in hand, with a slain giraffe went viral.
The announcement comes ahead of annual Boxing Day hunts across the country.
Fox hunting was meant to have been banned in 2002 but loopholes in the law mean that hunting still takes place
The League Against Cruel Sports is recommending a number of amendments which would tighten the loopholes