The giant biomedical charity already requires papers produced with Wellcome funding to be made open access within six months of publication, which is the period RCUK also mooted in its draft policy unveiled earlier this month.
But Robert Kiley, the trust's head of digital services, admitted that the current compliance rate of 55 per cent was "simply not acceptable".
He said many details of the trust's get-tough policy were to be determined, but one idea was to make institutions "take some responsibility" for the compliance of their Wellcome-funded researchers. He noted that open-access compliance at the trust's own Sanger Institute near Cambridge was 85 per cent.
He said the trust might require institutions to officially confirm that all publications associated with a grant had been made open access before the final instalment was paid. Another idea was to take Wellcome-funded researchers' open-access records into account when they reapplied for funding and activate further grants only once their previous research was openly accessible.
The trust also intended to follow RCUK's lead and require papers to be published according to the terms of a Creative Commons "CC-BY" licence, which allows unlimited reuse of content subject to proper attribution to the original author.
Mr Kiley said this would encourage the widest possible dissemination of research, such as via translation or by being posted on other websites. He said there were "clear parallels" between the trust's policy and that proposed by RCUK, which was criticised last week by the Publishers Association for disregarding publishers' concerns.
He said the two organisations, both of which offer to pay their researchers' open-access fees, aimed to approach publishers with a "common voice" over the precise licensing terms they expected.
Mr Kiley added that a wholesale transition to author-pays open access was inevitable. "It is just a question of how we get there," he said.