BII chief Neil Robertson says the standard of pubco codes of practice being submitted for rubber-stamping by the trade group is "encouraging".
Charles Wells, Fuller's, JW Lees, Everards and Elgoods have all had their codes "agreed in principle", but Batemans remains the only company to have had its codes signed off.
The process, being run by the BII's Benchmarking and Accreditation Services (BIIBAS), is designed to tighten up on clarity and transparency within pubco codes of practice for new and current licensees, after the BII scheme came in for criticism from MPs investigating the pub industry.
MPs from the Business, Innovation and Skills Committee (BISC) have even attended a benchmarking meeting, the BII revealed, and the group plans to bring in other people from "within the industry" onto the committee.
Neil Robertson, BII chief executive, said: "We are making good progress, all of the larger pub operating companies have engaged with the BIIBAS process and the standard of code coming forward is encouraging."
Bernard Brindley, deputy chairman on the benchmarking committee, said it is due to see McMullen's next week and has also received drafts from Scottish and Newcastle Pub Enterprises and Greene King.
And Enterprise Inns and Marston's are expected to submit draft versions of their new codes within the next two weeks.
Brindley described Punch's decision to consult their licensees over its code as a "good move".
He also revealed the committee were giving leeway to smaller companies in relation to next month's deadline.
"Pubcos with more than 175 pubs must get their codes to us before June 30, but we are giving some leeway to smaller companies," he said.
Brindley admitted that some pubcos were waiting to see details of RICS' new code of practice on rents.
But he added: "If there's any shocks in the RICS code, we can adjust things, but we don't anticipate that.
"Overall we're happy how things are going, but would still encourage companies to get us their codes as soon as possible."
For more information visit: www.biibas.com