Labour MP Perkins last week stood against Mulholland, the Liberal Democrat MP for Leeds North West, for the position of chair of the group that Mulholland himself had set up in 2009.
Perkins was ultimately elected as chair, but Mulholland has said that he plans to remain a member of the Group and as active as ever in his campaigning for pub rights.
"It is essential that we work together," Mulholland told The Morning Advertiser (MA) before adding that he would now be putting even more focus into chairing the British Pub Confederation - the group of politicians and campaigners that fights for independent pubs.
"Toby [Perkins] will regularly meet with me and other representatives of the British Pub Confederation.
"I wish to see the APPSPG carry on being a success and I will contribute where I feel I can be helpful. Toby has to lead and I don't want to make that difficult by interfering."
Mulholland, who was first elected as an MP in 2005, says he set the group up after being elected to Parliament because he didn't feel there was enough Parliamentary campaigning for pubs.
"I joined the beer group after being elected as an MP in 2005 and it became increasingly clear that there wasn't anyone who was campaigning on the issues that were leading to the closures of pubs; there was no one raising pubs in the planning system. Issues on pubs were not being raised adequately and there needed to be some proper campaigning that took on these issues," he said.
"I am very achievement driven and that is why it was set up as a campaigning group and that is something we have done very consistently. We set out to have success. If the things we campaigned on hadn't led to changes then I would regard that as a failure so I'm pleased that we have had successes."
The outgoing chair added that he felt Perkins, who was shadow pubs minister for the Labour Party from 2011-2015, shared his ambitions for the group and that it would continue campaigning on the issues leading to pub closures.
"I would not have wished to hand over the role to anyone who doesn't share the views that we have laid down as a group. We do have a list of policy objectives that we wish to see action on and in the case of Toby he shares those objectives and we will continue to campaign together.
"I think he is someone who has genuine interest in pubs, supporting licensees and is well aware that we need changes from the Government on planning because the current situation with assets of community value is not sufficient to stop predatory purchasing.
"I'm also aware that he knows the current pubs code is not working the way it should because of the actions of the pubcos. I do very much welcome that there will be another MP speaking out loud and clear on these issues," Mulholland said.
The MA understands that Mulholland and Perkins will meet in their respective roles for the first time on Tuesday (17 January) with the upcoming debate on pubs code adjudicator, Paul Newby, top of the agenda.