You state the £11,300 is your emergency fund that you wish to trim. How much would you consider withdrawing? I assume you are not going to invest your entire emergency fund.

What happens to the remainder? Does it continue to earn 2.3%, or do you have to find some other arrangement, such as sitting in a bank account earning next to nothing? Suppose you withdraw and invest £5,000, and the remaining £6,300 earns zero. Your invested money would have to earn 6.6% to break even. That is doable but by no means a certainty.