The Shrewsbury and Atcham MP recalled the exchange while speaking to Colin Murray during his show on BBC Radio 5 Live on Tuesday night.
Mr Kawczynski was a guest on a night the first flurry of ministers, led by Chancellor Rishi Sunak and Health Secretary Sajid Javid, resigned from the Government.
In a lively debate, Mr Murry quoted Theo Clarke as she quit as Trade Envoy to Kenya, who pinpointed the decision to promote Chris Pincher to Deputy Chief Whip as the main reason for her resignation.
He said: "When I was in Currys in Shrewsbury, on Saturday, buying a new vacuum cleaner, I had three employees in that building come up to me and say 'you've got to stand by Boris, you've got to back Boris'.
"I've never come across people coming up to me in an electrical store asking me to support any other Prime Minister that I've come across."
"So if three had come up to you and said don't back him and ask him to resign would you have done that based on three employees in Currys?", responded the presenter. "I mean come on. You're giving me poppycock."
Mr Kawczynski defended himself, adding: "That actually happened, that's not poppycock. I'm relaying the story"
After being asked if he was deflecting from the subject of Ms Clarke's resignation, the Shrewsbury MP replied: "I'm giving you a story that in my consistuency on Saturday when I was not performing my role as a Member of Parliament, but I happened to be in Currys in Shrewsbury buying a new vacuum cleaner, but people happened to recognise me as being the local MP, and they came up to me and they said 'please back Boris'. Now, that is the truth.
"Why were you so flabbergasted and angry about me relaying an incident that happened to me in my constituency?"
Mr Murray told him it was because he was talking about "three people who sold you a vacuum cleaner over a specific question about the reasons an MP has withdrawn her support for the Primer Minister".