Agree fully with the reasoning in Mike Scott's answer. As a small addendum, given the relatively low interest rates at the moment (2020), one option you might consider is NS&I Premium Bonds1.
Savings in Premium Bonds are backed by the government, so are at least as safe as a normal savings account (up to the maximum holding of £50,000). The "interest rate" (used to fund randomly-drawn prizes, instead of being paid directly) is broadly comparable with easy-access savings accounts2.
The main downside is that because the smallest prize is £25, if you've only got a modest holding, you cannot guarantee winning the equivalent "interest rate" that the prize-fund represents. For example, with £2,500 in a savings account at 1% interest, you would get a guaranteed £25 after a year. With Premium Bonds, because prizes are drawn at random, you cannot guarantee getting one win a year. However, with a more substantial holding, you will get closer to the "true" interest rate more consistently (sometimes above; sometimes below).
And, of course, there's always a chance that you will win a higher-value prize, well above anything you'd get in interest. (In 2004, one person one £1M with a holding of just £17). When I first had "spare" money available, the possibility that I might "win big" was a great incentive to save it (in Premium Bonds) rather than fritter it away, especially when the guaranteed return from a regular savings account would be so low.
1 Disclaimer: Although I've suggested Premium Bonds a number of times on PF&M, I have no affiliation with NS&I, other than being a customer.
2 As of September 2020, the prize-fund rate is 1.4%, dropping to 1.0% in December. MoneySavingExpert is currently showing the best instant-access savings account at 1.1%. (You can get 1.21% with 120 days notice, or 1.5% for a three-year fixed deposit, but those aren't really suitable for a "rainy day" fund).