Durr, who also played PC Mike Bradley in Heartbeat, lives in Malmesbury with his wife Kate, who often shares photos on Instagram of their stunning garden.
He joined other Casualty cast members, via a temperamental video link, after winning the Bafta TV award for soap and continuing drama.
Casualty saw off competition from Coronation Street, EastEnders and Hollyoaks to claim the award.
Speaking on behalf of the cast, William Beck, who plays Dylan Keogh, said it was a “huge honour” for the soap to win the award.
‘A huge honour for Casualty, and one we not only share with our fellow nominees in continuing drama, but also in the wider industry, both past and present, and the people without who we would have no show: the NHS."
He added: “The every day has been uniquely and tragically dramatic and each of us regardless of age, ability, gender, nationality have been forced to find a hero."
After the ceremony, Durr tweeted: "We did it! Trophy So proud of the BBCCasualty team winners!!! Thank you @BAFTA #VirginMediaBAFTAs."
The show was initially forced off the air due to the pandemic, but returned to screens in January.
Casualty went on to follow storylines like shortages of PPE, pressures on the hospital's emergency service department, and the impact of long hours on staff.
The actors chose to pay tribute to the NHS with their speech.
He joins his sister, Daisy May Cooper, who plays his cousin in the Northleach show and won best female performance in a comedy programme in 2018.