Savings of £18k is great - well done.
Now you've got into the habit, keeping it up will get you into an even better position - but you can definitely ease your foot off the pedal and do some fun things too.
You shouldn't think about stocks & share type investments for your emergency funds. The market is volatile, and the whole point of an emergency fund is that it's available to use immediately in an emergency - not just when the market is up. So keep that part in cash, in a high interest account - either instant access or a notice account that lets you get the money immediately but with a penalty on the interest payment. At the moment there are good rates on cash ISAs, but they only have an advantage if you'll be getting more than £1k a year interest- if not, there's usually a better rate available on an ordinary savings account.
Usually the recommended amount for an emergency fund is around 6 months spending, but you may want a bit more if your employment is at all unreliable.
Then plan for any known big spends coming up - expected car or house maintenance, fixed rate coming to an end on mortgage or 0% credit card.
What's left over after that is what you can think about investing with. Stocks and shares ISA (you can have this as well as a cash ISA, as long as you don't put more than £20k a year into the 2 combined) or pension (or both). At 38 there's still just time to open a LISA, which gives you a hefty bonus on savings of up to 4K a year (deducted from your £20k total ISA allowance), but locks the money away until you're 60.
How about taking the amount you've been saving every month up to now, and splitting it into 3? Use 1 part for pension (you save tax on money that goes into this, so the pot increases faster), 1 for other investments, and 1 part goes back into your spending pot.