Benefits of paying off mortgage

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I am going to start by saying that I know I am in a very fortunate position but could use some advice from somebody who can see a wider picture than I can!
I have a rare thing called an offset mortgage that is due to run for about another 10 yrs - basically whatever I have in savings is offset against what I owe on the mortgage & I don't pay interest on that (but equally I don't gain interest on the savings). I can draw out of the mortgage pot at anytime, I'd just pay interest on the difference between the amount owed & the savings. I am now in the position where my savings are almost equal to the amount left on the mortgage.
What are the benefits to somebody in my position of paying off the mortgage in full vs leaving say £10000 outstanding with that in the savings account so paying 0% interest & just letting it drift for a while? (Or maybe just paying off £100 a month against the remaining capital).
I have a rare thing called an offset mortgage that is due to run for about another 10 yrs - basically whatever I have in savings is offset against what I owe on the mortgage & I don't pay interest on that (but equally I don't gain interest on the savings). I can draw out of the mortgage pot at anytime, I'd just pay interest on the difference between the amount owed & the savings. I am now in the position where my savings are almost equal to the amount left on the mortgage.
What are the benefits to somebody in my position of paying off the mortgage in full vs leaving say £10000 outstanding with that in the savings account so paying 0% interest & just letting it drift for a while? (Or maybe just paying off £100 a month against the remaining capital).
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The exception to this might be if you are anticipating something happening in the future where you think you might need to access your savings?
If not, then how would you benefit from keeping £10,000 savings in an account bearing 0% interest, just to accompany a token mortgage amount?
Does the offset mortgage provide you with any other benefits that are helpful to you? If so then that could also be a reason for keeping a small mortgage balance outstanding I guess.
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