Overpaying a mortgage over 100% LtV is throwing away money. If you think there is a risk of going into negative equity, best to keep your money somewhere else so you can cut and run from the property if needs be and come out with some savings.
?? Under the UK mortgage system a debtor is liable even if the property value is less than the loan. You can't cut and run from the debt without bankruptcy or a CVA etc, can you?
It is different in the US where your advice would hold true...
If you're staying in the same place then it doesn't matter whether you overpay now, later or not at all.