"I bet he can't, because there isn't any," Boswell said.
Last week, Vicary-Smith said he would not put CRUK's name to a collaborative public education campaign, organised by the Institute to defend face-to-face. He told Third Sector that public confidence was a much bigger issue than any short-term financial gain.
Boswell said he was writing to Vicary-Smith to ask him to provide evidence to support his statement about the erosion of public trust.
"I think that is an outrageous approach. As I said in my last Third Sector column, if someone really thinks it is unethical then they should do something about it.
"He has not made any statement, nor has he spoken to the Institute about any problem he has with the Codes of Fundraising Practice. CRUK is an active member and gets consulted along with every other member on the codes, and if he genuinely feels that face-to-face is undermining public trust, then he needs to do something about it and not just be passive.
He should be actively campaigning to get it changed."
Boswell said he "totally respects" CRUK's decision not to do face-to-face, and understands that the charity's huge income from other sources, such as the Government, companies, and the public, meant face-to-face wasn't as essential for the cancer charity as it is for some others. But he added: "It would still be interesting to look at how many more millions would have gone into cancer research if CRUK had entered into face-to-face at the same level and at the same time as Barnardo's."
Vicary-Smith declined to comment further until he had received Boswell's letter.