Even if savings aren't expected to grow, and may even lose their purchasing power, you should still aim to have some cash available for annual and irregular expenses plus a cushion in case of income loss. How much this needs to be obviously depends on your fixed costs and job stability.
A frugal person with low bills and a very stable job would need less ready cash than someone who may lose a high paying job and need to keep paying a big mortgage etc and might struggle to find a similarly paid role, especially in times like these where you might have more people competing for fewer jobs.
As you might need this money quickly, it needs to be cash or cash like as you don't want to have to access investment income when the market is low. Eg if someone had £10k in a FTSE tracker fund at the beginning of this year, it would have lost around a third of its value by mid March, when it became clear how bad coronavirus was going to be. It's recovered a bit now, but I'd regard the stock market as extremely volatile for the next few years at least. Unless we get negative interest rates, your cash at least keeps the same value, even if it doesn't have the same purchasing power.
As for interest rates, you can still get slightly over 1%, so all those who've received letters from your savings provider telling you that your interest rate is now 0.1% or whatever, look at moving your money. But it's up to you whether you decide that it's worth the effort - 1.2% on £10k is £120 per year and it's not taxable unless you have a lot of savings and are a very high earner. On 0.1% the annual interest is £10 per year.
I'm in two minds about premium bonds. The closer you get to the maximum, the more chance your prizes will match the average payout of 1.4%. If you have less than £10k, with average luck, you could get little or nothing, or you could get a few extra prizes and get more than this, plus there's also the admittedly very small chance of getting a much bigger prize. So you're effectively gambling the interest that you'd definitely get in a savings account against the chance of getting a better return, with no risk to your capital. You can also get the money back within about a week, so almost like cash.
You should only put money at risk if you can afford not to touch it for several years or more because it could lose a lot of value. Over time the stock market should go up more than cash, but it's far from guaranteed, so you need to avoid having to take it out at a certain time, in case that time coincides with when the market is low, like now. Anyone who put all their money on the stock market and has now lost their income, faces losing a lot of money if they need to sell investments now.
Paying off any debt, including mortgage debt, is usually a good thing, as it reduces your outgoings, and the interest rate may be higher than what you get on savings, but it's not always the case. Some debt attracts zero or very low interest, such that you can sometimes beat the interest rate, even with cash savings. Eg our mortgage interest rate is currently 0.5% but we're getting 1.2-5% on savings, so not rushing to pay the mortgage off, but have money to throw at it any time that the balance tips the other way, plus it allows unlimited overpayments so the money can be moved over at any time.