A press conference led by Piddington Parish Council chairman Tim McNally took place on Friday after Housing Secretary Angela Rayner approved the Home Office’s application to change the use of the site for asylum accommodation.
The Home Office said this would allow it to continue developing the plan but that no final decision on the site had been taken.
There has been significant local opposition to the proposal and a legal challenge to the planning decision is expected from the parish council.
In September, Piddington symbolically voted to leave the UK over the planned use for the site in Oxfordshire.
Politicians from the Conservatives and Reform have made several visits to Piddington, a village of about 350 people, to show their support for campaigners.
Speaking on Friday, Philp said a future Conservative government would shut the asylum accommodation “straight away” if it was opened by Labour.
Yusuf made clear Reform’s opposition to the plans before his focus switched to the Conservatives.
He said: “It’s obviously true that we would not be gathered here today and 1,200 men would not be being dumped into this beautiful village were it not for the actions of the Conservative government.
“So I actually want to ask you Chris, would you actually like to apologise for the things you did in government to bring hundreds of thousands of people into this country illegally?”
Philp, a former immigration minister, described Yusuf’s remarks as “disingenuous” and argued the migrants who could be housed near Piddington will have arrived in the country while Labour has been in power.
He said the Conservatives are under new leadership and he hoped the politicians could “stand in solidarity with the residents” rather than “engage in point scoring”.
Philp added: “Zia, read the room, listen to the people clapping and read the room.”
Yusuf countered that it was “important that we hold everybody accountable for this situation” and said Philp had been “heavily involved in immigration and borders policy” for the Conservatives in government.
Philp repeated his “read the room” suggestion, adding: “The public here want you to pipe down on the cheap politics.”
Yusuf dismissed the suggestion that he was engaging in “cheap politics” and repeated his criticism of the Conservatives’ record, saying they “refused” to secure the country’s borders when in power.
As Yusuf spoke, Philp could be heard saying: “Buddy, I’m not here to give you comms advice, mate, you’re in a hole stop digging.”
Philp told Yusuf he should “calm down”, with the Reform politician repeating his request for the Conservative MP to “apologise to the British people”.
McNally thanked the pair for attending the press conference, adding: “I understand this is a passionate discussion and I respect you both for what you’ve got to do and what you represent.”
While the two parties are on the right of politics, it is unusual for them to share a platform to campaign and both are keen to stress their differences to voters.
Reform leader Nigel Farage has pitched the party as replacing the “old, fuddy-duddy” Conservatives, and Tory leader Kemi Badenoch has said she would rather have another general election than do a deal with Reform to secure power.