An idea

Rather than adding an extra hurdle could there not be some incentive to use said currency, for example a discount applicable only to that currency?

In the modern age one wishes to be able to use ones specie to purchase anything, anywhere, often at the drop of a hat.

A currency that restricts me has no utility or attraction, whereas something based on firmer foundations than GBP has a strong attraction.

The attraction of local currencies is that they support the local economy, which is something many people want to do. If you don't care about the local economy then it has no attraction for you.

If you are looking for something that has firmer foundations than GBP then the EUR or USD (and possibly the CHF) are about your only options. Assuming that your money is currently GBP however, the conversion is gonna hurt you.

Offering a discount for using local currency may attract trade to your area, but the vendors will take the hit in the long run (I doubt there are many wholesalers who will accept the Lewes or Brixton currencies). Like any discounting scheme, they would need to be sure that the increase in volume would account for the drop in per-unit revenue.