Beg, borrow or steal a copy of Investment Made Easy by Jim Slater if you can. It's likely to be out of print, so start with second hand booksellers or Amazon. Take it on holiday and read it carefully, maybe twice. It is very clear and explains how to start thinking about money and investment, and how a portfolio is structured. You need to know enough to ask confident, informed questions of professionals and if you are asking us, you clearly are hesitant. Park the balance in a bank (after paying off mortgage) until you feel ready to tackle the next stage.
Ask around among the most successful people you know to find out who advises them on investment. There are good ones everywhere, but more bad ones.
Otherwise, you might consider the new generation of low-cost indexed managed funds, like Vanguard, which charge a lot less than 1.5%. I'd pick several and split the nature of investments between equities and bonds. At your age, you should have some with a 30 year horizon for retirement, probably equity-based with the primary aim of capital growth, and risk profile reduced by investing in different industry sectors, or by region; as well as some elements thinking shorter term (say 5-10 years) so that you have freedom to work a bit less if you decided. From what you say, you don't really need to top up your current income.
You say your ISAs are maxed out. but you can put £50K into Premium Bonds and use that as instant access emergency money if you need it. Bank interest rates are rubbish, although likely to start rising before Christmas, but it isn't likely to feed through to savers very soon.
Jim Slater is a bit dated; the book was published in the early 1990s, but investment thinking changes less than the newspapers would have you believe. You already know the most important ideas:
If it sounds too good to be true, it is!
There is no free lunch.
If you don't understand the risks, and someone tells you there isn't one, run.