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If you have (say) a 300,000 mortgage and you can pay back 10% a year without penalty then unless you think you can pay back more than 30,000 in a year you can overpay at any time within the year that you see fit, so why not earn more from your savings and overpay the day before the anniversary if that's what you want to do?
Check the details of the overpayment limits. Ours (Santander) is 10% of the outstanding balance per calendar year. So whilst you can pay £30k (in your example) in the first year, it will be less than £27k the year after, etc. Unless you want to be paying back a very high percentage each year it's unlikely to be a problem as you'll be through the limited overpayment period before the limit gets too low.
Also, it doesn't have to be a "fixed or offset" choice, there are such things as fixed offset mortgages. Having one of them from the start would have really suited us...
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Greenbank
If you can get more in interest from savings then you might as well put your money there.
If you have (say) a 300,000 mortgage and you can pay back 10% a year without penalty then unless you think you can pay back more than 30,000 in a year you can overpay at any time within the year that you see fit, so why not earn more from your savings and overpay the day before the anniversary if that's what you want to do?
Alternatively you can take the view that overpaying is effectively the same as having a shorter mortgage term. With that proviso, you could take the mortgage out with the longest term you can get and then choose to overpay to bring the term down to what you actually would rather have.
This all gets more complicated when you factor in the various ways you can be charged interest. If you're on a fixed deal and looking to remortgage when the deal ends, then it might be useful to overpay to get to a particular LTV threshold to get a better deal. You also typically pay a penalty to cancel a fixed term early and that penalty is often a percentage of the remaining loan - overpaying to reduce that prior to cutting ties is maybe a way to save some fees (although you'll lock away your cash). If you're on a variable rate then you may as well put your money where you get the most interest and re-evaluate as rates change, I suppose.
I'm not a financial advisor, just outlining the various scenarios I've been playing through in my mind.
If you're on a fixed deal now, even though the early cancellation fees are eye-watering, they can still be a net win if you switch - do the math, as some might say.