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Without knowing what the lumpsum is in relation to 35% its hard to give an accurate answer.
Do neither and just live in the place as planned
Given the uncertainty this is the safest strategy.
The advantages of overpaying are 1) guaranteed gain from long term interest savings, and 2) improving LTV for future remortgage.
You can work out 1) and decide if that is a better return vs savings, ISAs etc.
If the lumpsum is big enough to move your LTV into another category then it maybe worth considering. If it isn't then its irrelevant.
A bigger factor tho is I'm assuming the bulk of you and your partner's net worth is in UK property. If this is the case a large overpayment will further reduce any diversification you have. Generally diversification results in the best performance long term as it reduces losses.
Ok, with all this house price drop talk... say worst case happens and we are all down 35%, what would the best thing to do with a large lump sum? Over pay before? Over pay after? The lump sum is from capital on another sale. Do neither and just live in the place as planned? Brexit really is a pain in the arse...