One thing to remember about reusing bags is that they can become contaminated with some nasty stuff over time, so don't forget to wash them or bin them.
But our local council refuses to accept them in recycled bags as "they clog up our multi million £ waste-sorting machine". So "take them them to your local store and recycle them there".
I always shop with a knapsack with a few bags-for-life inside. I haven't paid for a single 5p bag. And the bags-for-life came out of the recycling bin at the shop entrance.