I too think some kind of permit would be a good idea, as I agree with Sparkles that it is very frustrating when you have small children and bags of shopping, or a pregnant partner, and having to park streets away and make multiple trips from the car to the house and back, especially in the cold and rain!
Maybe permit only Mon - Fri, for a couple of hours during the day would be an idea. That way commuters can't park there all day, but people can still come and use the shops on the parade outside of those hours.