Really interesting question. The allergen is not stated in legislation as "Gluten" it is "cereals containing gluten" which includes wheat and barley.
1. Cereals containing gluten (eg wheat (such as spelt and khorasan wheat), rye, barley, oats, or their hybridised strains), except:
(a) wheat-based glucose syrups including dextrose
(b) wheat-based maltodextrins
© glucose syrups based on barley
(d) cereals used for making distillates or ethyl alcohol of agricultural origin for spirit drinks and other alcoholic beverages.
As they are listed under the same subset, in this case, I would not control them differently, I think, however, I would ask advice from the retailer if they are a retailer brand.
Why do I say "I think"? Well I have first hand experience nowadays with allergens as I have two close friends with allergies and my son. One of my friends is allergic to wheat and, now, he thinks other items containing gluten. Initially his diagnosis was only for wheat though which is making me wonder two things; do factories control the two together and that's why he's reacted to barley products? Or is everyone who has an allergy to wheat also allergic to barley?
The other reason why I'm a little unsure is that I know from first hand experience how allergies can be treated as one block which annoys the hell out of me. My son is allergic to two specific tree nuts for example and not others and not peanuts. So if a factory control peanuts using the same scoop as they'd use for one of the treenuts he has an allergy to, then he may have a reaction. Likewise if they use the same scoop for hazelnuts which he's not allergic to and one of the ones he is, that could be an issue and they are all in the same category of the legislation.
8. Nuts, i.e. almonds (Amygdalus communis L.), hazelnuts (Corylus avellana), walnuts (Juglans regia), cashews (Anacardium occidentale), pecan nuts (Carya illinoiesis (Wangenh.) K. Koch), Brazil nuts (Bertholletia excelsa), pistachio nuts (Pistacia vera), macadamia nuts and Queensland nuts (Macadamia ternifolia), except:
nuts used for making distillates or ethyl alcohol of agricultural origin for spirit drinks and other alcoholic beverages.
But allergic consumers would avoid all nuts right? Wrong. In fact, the current medical advice my son has been given is to actively eat the nuts he's not allergic to in order to make sure an allergy doesn't develop.
I appreciate nuts and gluten containing cereals are not the same thing in terms of likely reaction, however, anaphylaxis to wheat and gluten containing cereals can occur as has happened with my friend. I suppose the difficulty is every test will test for gluten.
Some specialist advice is needed I think? Ultimately I might be getting into a twist because the allergenic compounds in both wheat and barley are identical but better to get something official to confirm it because, as I've found, allergic response between nuts is definitely not identical so I wouldn't assume.