There's a few things to consider here.
Is it 10% per year of the anniversary balance or 10% of the original loan.
Example my current mortgage is 10% of the anniversary balance, the mortgage I am moving to is 10% of the opening balance so while the first decreases the second stays fixed.
Generally speaking overpayments are for a given period and you will only trigger charges if you go over your entitlement in the period, so yes you can pay your 10% overpayment all in one go.
As for saving thousands on interest that's not really going to be the case. Doing some rough calculations I have assumed an 11 year period at 1.29% based on payment amount and principal. This would mean £3.8k total interest over the period, if you retained the same rate.
Adding in your planned overpayments you will save around £2k in interest, but you need to factor in what interest you would be able to earn on the money if it was in fix rate bonds/ISA's etc and off set that.
At the end of the day, overpayments while rates are low is the best low risk way to benefit. Also means your mortgage gets paid off a lot sooner, in the example given its 7 years instead of 11 with your plan.