I’ve only been to the Dutton’s Chester restaurant and loved the atmosphere, location and friendly staff there. And as an additional, and likely most important factors, the food is pretty amazing.
Gluten free? It’s not clear online, but Duttons do offer a gluten free menu so be sure to ask if that’s applicable to you! The menu is broken down into nibbles & small plates, sharers, mains & salads, sides and desserts. If you’re gluten free and vegan options are limited, however discussion with staff on a few options may make them suitable for you!
Vegan? I didn’t eat at the restaurant when I was vegetarian, however upon looking at the menu, there are a limited number of options which are vegetarian. Some of these are clearly not suitable for vegans, whereas with other options it would be worth checking the extras on vegetarian dishes, e.g. possibility of dairy in coleslaw, or removing an ingredient.