The Road Haulage Association, the trade body representing freight companies, said Mr Grayling threatened to stop involving the organisation after they communicated with the press following a private briefing with the Transport Secretary last August.
• READ MORE: Brexit: David Mundell urged to quit Cabinet to prevent no-dealIn a BBC Panorama documentary, which is due to be aired on Monday, Richard Burnett, chief executive of the Road Haulage Association, said Mr Grayling left him a voicemail after the association issued a press release about the meeting.
In the voicemail message, Mr Grayling said: "I've got to say how very disappointed I am.
"I had intended to involve you closely in the planning over the next few months, but issuing a press release straight after meeting like that makes it much more difficult for me to do that."
Mr Burnett said he felt Mr Grayling was "trying to silence an industry that's trying to help Government guide them".
He added: "My sense of that message was - either shut up or you don't engage.
"You either play ball with us or you won't be part of the negotiations on behalf of the industry."
The Road Haulage Association has acknowledged that discussions with the Government have continued after the voicemail message was sent.
"It is extremely unfortunate when details of private conversations held in confidence are made public in a press release."
The documentary will also feature an interview with the former permanent secretary at the Department for Exiting the European Union, Philip Rycroft, who told BBC Panorama that a no-deal Brexit is something the public should be "worried" about.
Mr Rycroft said: "I think everybody should be worried about what happens in a no-deal situation. We would be taking a step into the unknown."
He added: "It's not in the UK's interest to have no-deal, it's not in the EU's interest to have a no-deal.
"The rational outcome over the next few months is to get a deal because that is overwhelmingly in the economic interest of both the EU and the UK."
Mr Rycroft was in charge of Brexit planning for 18 months before stepping down just before the March Brexit deadline.
He said there are around "16,000 civil servants whose jobs are dedicated to Brexit-related issues", in what he calls "an unprecedented situation" and "the biggest exercise across Government we've seen over the last few decades".
He added: "The planning I think is in good shape, absolutely... but of course what that doesn't mean is that there won't be an impact from Brexit, and particularly a no-deal Brexit, because that is a very major change and it would be a very abrupt change to our major trading relationship."
The programme will also look at security concerns related to Brexit.
Assistant Chief Constable, Tim Mairs, of the Police Service of Northern Ireland (PSNI), warned Brexit could provide a recruitment "opportunity" for the New IRA and other dissident paramilitary groups.
He said: "We know that the New IRA and other groups continue to recruit people and we believe that Brexit provides an opportunity for them to encourage people to recruit."
He added that currently, the PSNI does not see any upsurge in recruitment or violence being driven specifically by Brexit.
Asst Con Mairs also explained the fears that potential price differences on the border created by tariffs could create "new opportunities" for organised crime groups to exploit.
He said: "We would see, traditionally, connections between some of those groups and more violent groups."
He added: "The potential impact of a no-deal on the economy in Northern Ireland is significant and that would, in our view, present potentially significant security concerns moving into the future."
The BBC Panorama programme No-Deal Brexit: Are We Ready? is set to air on BBC One at 8.30pm.