The call comes after the group released its half year results, which reportedly highlighted the "continuing major effect" the measures are having on the travel and tourism sector.
Figures for the first six months of its financial year showed MAG passenger numbers remained 82% down on pre-pandemic levels, despite initial early signs of recovery over the summer.
MAG airports welcomed 6.6 million passengers between April and September, compared to 36.4 million for the same period in 2019.
The group, which owns and operates Manchester, Stansted and East Midlands airports, saw year-on-year revenues increase by £64.9 million, but the figure was down 70% on the same period two years ago.
Overall, MAG reported a loss before interest and tax of £75.7 million for the six-month period. By contrast, the group returned £172.7 million in profit for the same six months in 2019.
MAG’s half year results cover the period 1 April - 30 September and were released after travel restrictions were reintroduced for passengers following the identification of the Omicron variant.
The government’s decision to bring back both Day 2 PCR and pre-departure testing for all travellers to the UK will, according to the organisation, "hold back the recovery" of international travel and the UK aviation industry.
MAG chief executive Charlie Cornish said the first half of 2021 "tells a story" of how travel restrictions "held back" the recovery of UK aviation, "especially when compared to the rest of Europe".
“As restrictions eased, passenger numbers grew steadily at all three of our airports," he added.
"The reintroduction of costly and inconvenient travel testing requirements has created further uncertainty and delayed our recovery.
“The government has talked openly about the damage these restrictions cause to the travel sector, but neither they nor the opposition have recognised the critical need to support our industry in return."
