Yes they do roll and they will show quite often.
Like all Cyprinids they have to maintain their buoyancy via the swim bladder, as pressure changes and river levels go up and down they must adjust the amount of air in the swim bladder, to eject air they can “burp” air out as the swim bladder is connected to the alimentary canal via a pneumatic valve, however to gain air they must take it in, the only way cyprinids can do this is to go to the surface and gulp down a mouth full of air and force into the swim bladder via the pneumatic valve.
You might have noticed in still waters Tench and Carp will roll which will be followed moments later by a string of bubbles, this is caused as the fish takes in air, adjusts the pneumatic balance and then ejects the air it does not need.
This is often done as the fish start to feed, I suspect this buoyancy adjustment is needed because the fish are starting to be come active.
Barbel are no different, however due to an under slung mouth their roll is distinctive because you often see a fin show during the roll and it is very often followed by a small splash as the fin (I think it is a pectoral fin) hits the water, (I did have a short film of Barbel rolling in the Thames but I can’t find it at the moment).
Fish like Pike, Perch and Zander do not have a pneumatic duct they can only introduce gas to their swim bladder via their bloodstream, this gas is mainly Oxygen, which is why many of the original experiments using Oxygen were conducted once a few Perch swim bladders had been obtained (Perch swim bladders contain about 70% Oxygen, a much higher percentage of Oxygen than air which only contains 20% Oxygen.
On rivers where there is a lot of Streamer Weed (a rare sight in the south these days, Streamer Weed was plentiful in the past) you will often hear a sucking noise, this is caused by Barbel, I am not sure why they do it but it may be simply for pneumatic balance or they might be feeding on something in the weed.
In rivers where there is a lot of mud or silt on the bottom Barbel will fizz like mad as they cruise up and down, this is a dead giveaway and when you see it get your gear out.
I have often watched this happen; the fish will often cruise up and down in pairs or groups of three, passing over the same area time after time.
In this picture you can clearly see two fish side by side moving up stream.

In this picture the Barbel is getting stuck in big time.

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