As far as I know, every police force will take any firearms you wish to surrender. Possibly not a good idea to stride into a front counter waving your gun around though. I would suggest you call them first (if you can get an answer) in case they want an authorised person there (an FEO or AFO or someone) to ensure it's safe. But in any case, bring it in a slip and with the bolt out or whatever shows it to be not loaded.
The problem these days is that, especially with shotguns, there's now far too many run of the mill old guns that are arguably not fit for non-lead shot and aren't worth a dime. Once upon a time you could sell them for a few quid, but really nobody wants them now. In a lot of cases, you would even struggle to part-ex them for a new purchase. Or the part-ex figure will strangely be the same as any discount you might get without a part-ex.
So, although it goes against the grain, sadly the easiest way to get rid of pretty worthless firearms is to give 'em up to the police. And usually, unless there's a gun of some historical importance or value, (and someone recognises that, which they may well not) anything you hand in will be destroyed. The thinking behind the policy is that these firearms aren't going to fall into the wrong hands anytime.