I will let someone else answer pensions as I do the bare minimum there!
With savings, if you can confidently put any of that away in a fixed rate ISA, I would do that first.
Because that's tax-free, i.e. you don't have to pay tax on that and the interest - and I would fix the rate for however long you can lock the money away.
If that uses your total savings, I wouldn't put it all in there - leave some for emergency bills.
If you are under 40 and not a homeowner, you might want to make use of this particular type of ISA.
https://www.gov.uk/lifetime-isa
Generally at the moment I would look at a fixed rate for savings in case interest rates go down.
So after an ISA, I would look at easy access fixed rate.
Some instant access accounts are offering a very good rate and you can withdraw money any time. There's also some halfway house accounts where you can withdraw money with notice.
You could also feed some money from a current account into a savings account with a regular saver, some of which are paying good interest at the moment.
so it partly depends how much you've got and whether you're starting with a lump sum.
With the regular saver, if you need to cancel it because you have an emergency bill, you usually can.
With any high deposit, or indeed any financial institution, make sure they are covered by the Financial Services Compensation Scheme (FSCS). This will cover you up to 85,000, so if you have more than that try not to put it in more than one account.
They have temporary cover if you suddenly put a load of money in one place, e.g. after selling a house.
Generally, advice will vary depending on whether or not you're a very high earner and your age as well. If you are a very high earner, I am not the best person to ask!