But the overpayment only affects the amount overpaid and not the total mortgage. By my calculations:
Overpaying your mortgage @1.24%
After overpaying £1,000 a month for 3 years and 0 months, you'll have a total of £36,693 in overpayments including £693 in interest
Saving £1000 over the same period at 5%.
After saving £1,000 a month for 3 years and 0 months, you'll have a total of £38,731 including £2,731 in interest
So after 3 years you would be £2038 better off by saving rather than overpaying.
Yes it's true that you may hit the 10% limit so is a factor. Its also generally true however that once you overpay, that money is effectively gone and inaccessible (not always). For me personally I'd rather than the funds were available at the end of the period and choose whether to overpay, invest or splurge depending on circumstances at the time.
Different strokes and all that.