The London studio believes the 32-metre-wide Blackfriars Bridge could easily be reconfigured to create a public garden spanning the River Thames, providing a much cheaper solution than Heatherwick's £175 million proposal.
Like the Garden Bridge, it could offer a green oasis in the heart of the city with views of St Paul's Cathedral and other landmarks.
"A garden over the Thames is a tantalising vision, but it's one that does not require an entirely new bridge. We could simply use one that is already there," said Allies and Morrison in a blog post.
"The Blackfriars Bridge Garden celebrates our infrastructure heritage," it continued. "It does not require extensive construction and can be delivered at a fraction of the cost of a new bridge."
By combining the two pavements on opposite sides of the bridge into a single 14-metre-wide pathway, the studio claims there would be enough space to create a garden with an area of 40,000 square feet – approximately 3,700 square metres.
"Existing parapets provide lovely seating nooks, riverside alcoves for a sandwich at lunchtime, a break from a jog or a place for families to gather – a garden for morning commuters as well as the quiet moments of urban life," it said.
The Garden Bridge has been the subject of ongoing controversy, with concerns around funding sources, claims the procurement process was unfairly biased and issues surrounding the bridge's eventual use.
Critics claim that the structure will block views of St Paul's, that it will be closed at night, that cyclists won't be allowed to access it, and that it is a waste of taxpayers' money that could be better spent elsewhere.
Blackfriars Bridge could provide the answer to all of these issues, according to Allies and Morrison, and would also offer numerous environmental benefits.
"The intention behind the bridge is a noble one, but the widespread concerns about cost, ownership and appropriateness are hard to ignore," said the studio.
"[The Blackfriars Bridge Garden] would remain public and accessible to all, seamlessly integrated into the existing public realm on both sides of the River without obstructing any of its views of St Paul's," it added.
"This light touch approach would be carbon neutral, and together with the cycle superhighway and solar panelled roof of Blackfriars Station, would be at the heart of a global exemplar for sustainable infrastructure."
Heatherwick first unveiled his design for the Garden Bridge in 2013, in response to an idea from British actress Joanna Lumley.
He claimed the project would allow Londoners to rediscover the "amazing piece of nature" that is the River Thames.
It is scheduled to complete in 2018, in line with a strict timescale that requires it to be in place before work starts on a major new sewer. A building contractor has already been appointed, despite calls for the project to be halted from several key figures.
The structure is expected to cost £175 million, with £115 million from private donations and £60 million of public money already committed. The source of the remaining £30 million has not yet been revealed.