Given that you'll have equity in your current property so your new mortgage is unlikely to be greater than 92% (or the relevant max.) loan to value whether you use surplus funds to overpay or save on deposit, it doesn't really matter. In other words, it won't change the amount of mortgage you'll be looking for next time around whichever course you choose.
Advantage of overpayment is you benefit from a return on your "savings" thus employed equivalent to the rate you're paying on your mortgage (less interest relief if your annual interest bill exceeds the threshold).
Advantage of saving on deposit is that you will have cash to put down a booking deposit with estate agent or builder when you do find the house of your dreams in the future. Ideally you don't want to have to borrow to fund this because it costs money (obviously) and is unsecured borrowing which can take some explaining when applying for your next mortgage.
Make sure you're not leaving yourself cashless if overpaying your mortgage. You are in the fortunate position of living within your means and should put yourself in a position to benefit from that should the unexpected happen (i.e. you should have a pot of rainyday money to call on).
Equally, make sure you're not missing out on any obvious opportunities such as maxing your SSIA.
But overpaying's good and you won't find many people advising against it on this site.