I ignore all of the designations such as trap gun, upland gun, etc. For me what matters is the weight of the gun (a lighter gun is easier to carry but has more recoil-balance it out as you see fit. I like lighter guns around 6lb), the gauge (20 or 12 gauge for me), the shell size it can shoot (up to 3 inch for me. Because I like lighter guns, the 3 1/2 shells are too much for me), and it has to have interchangeable chokes. Other than that, the feel of the gun is what matters. I've shot some excellent guns that just didn't feel right for me. The designations just mean that the gun favors certain characteristics, but most of them can be used as an all around gun. For example, a turkey gun can usually chambers a larger 3 1/2 shell. That doesn't mean you can't put 2 3/4 shells in it and go shoot some rabbit. Trap guns tend to be heavier, so they have less recoil when you are shooting targets all day. I use an O/U for everything. When I'm out hunting turkey, people look at me like I'm weird, but I don't care. It works just as well as any other gun.
I don't know how it is in the UK, but here a lot of trap ranges have a patterning range where you can get a huge target and pattern your shotgun. 410 has very little stopping power at longer ranges. If you are looking for an all around gun, I would go with 20 or 12 gauge.