Overpaying off your mortgage to reduce the amount of interest you pay over the lifetime of the mortgage is a very good way of saving money in the long term. It also imposes discipline, if you have a problem with saving, as you cant dip into the savings.
However, this is a long term saving strategy. It is slow and expensive to liquidate those savings if you really do need them, adn there is a risk that the bank would refuse you a remortgage, leaving your savings completely inaccessable.
It is only appropriate if you have enough short term, relatively accessible savings for issues like car purchases, house repairs, and rainy day money for emergencies.
In short, Its a great idea, once you dont leave yourself with no other savings.