The ones that come through the door from eg AgeUK are clearly marked that they're for stock for the shops; they will be sorted and the rubbish will be sold by weight, but the rest is for shop stock.
Didn't know abut mencap but the dodgy ones are not charity names that are familiar or have shops, they're just companies trying to look like it's for charity. On the bag somewhere will be something like 'collect plc have been authorised by x charity to collect, and a percentage will go to them', or something like that - I haven't got any here at the moment to look at because those get thrown away.
Mostly we take our stuff to the shops ourselves but sometimes put some in the ageuk bags for collection.
Also of course if you take it to the shops then you can register for Gift Aid if you're a taxpayer, which means the shop gets a lot more money