Should I pay off my mortgage (2)?

I asked this question recently: Should I pay off my mortgage? — MoneySavingExpert Forum.  I am still debating whether to pay off the mortgage (value is currently £45K) or invest (buy a second property top let or invest in shares).

There was an interesting article in Investors Chronicle this week, which talked about this and an economist said that interest rates are likely to increase in the future so it may be more worthwhile to pay off the mortgage.  I still have 2.5 years left with my fixed rate of 2.75%.  .I was thinking about investing for the 2.5 years and then pay off the mortgage i.e. before the rate potentially increases, however I don't think that is a long enough time frame for investing.  Another idea is to pay off the mortgage now and invest the normal monthly payment in shares.

If I pay off my mortgage and find myself struggling (probably unlikely), then I guess I can take out a new mortgage at the end of the fixed term? I believe this is called an unencumbered mortgage.  My research is telling me that I would get the same or better rates than someone taking out say a 40% mortgage or less.  One report I read said an unencumbered mortgage shows financial stability, which banks look favourable on.

Is there anything else I should think about with an unencumbered mortgage?
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