How does inflation affect whether I should pay my mortgage off?

I am in a bit of a dilemma. I have savings in cash earning between 1% and 2%. I currently have a mortgage of £65K at 3.8% which I can afford to clear or reduce. I have always understood the more you can pay off the better.

I was going to remortgage reducing my borrowing to £35K keeping the remaining around for a potential renovation or overpayment (or being over cautious!). I have since been asked why I would reduce it now when comparing rates to inflation. I don't fully understand this.

My choices are clear my mortgage using my savings. 

Remortgage to a BTL around 2% reducing lending and the term. 

Remortgage keeping lending and term the same.

My mind is whirling.... Any help appreciated. Thanks 🙂
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