2people1bike demonstrates the problem nicely with this photo showing how to get a tandem past the barriers.
Cycle A 2 B has a couple of posts with clear photographs of the barriers, Fallowfield Loop 2 and Fallowfield Loop Barrier.
And, if you can cope with wobbly video from a head-mounted camera, there is also a video, though not of the section I cycled.
Here by comparison is Rowland Dye's rather better made timelapse video of the Bristol to Bath Railway Path - notice the lack of barriers along the path.
If you are yet to be convinced as to why all cycle routes like this should be open to non-standard pedal cycles then watch this programme - jump 17 minutes in to see just how important cycling is for people with a disability.
Interestingly CycleA2B contains this note
"As is this page where I found out there is actually a tunnel underneath Sainsbury's on Wilmslow Road, the design was a cock-up though so it's not in use."
Now, whilst the page linked to is no longer available, it links to this web site... http://www.steveessex.com/jobs/, a name which also turns up in this document about access barriers.
And this document contains a photo of the Fallowfield Loop which explains the horse shit on the path and, quite coincidentally, a photo of my Brox.