If you want big returns on your money, then why have you stuck it in a savings account? It is free money. Sorry but it is. It's pretty much risk free, assuming you haven't deposited more than £85k in each bank account. If you want to make big money then you have to take some actual risks, not expect big returns for putting your money in a bank account and expecting to just have access to it whenever you like!
I'm the first to encourage people to invest in equities if they want a higher rate of return. But you seem not to understand the basics of banking. Banks have to maintain certain liquidity ratios of assets to liabilities, or in its simplest form, savings to lending. Those savers enable you to have a mortgage. That's why you see some banks offering market leading rates on occasions to increase their deposits,
It's not about risk, it's about opportunity cost. If I put that money in a savings account, I'm losing the opportunity to invest it in other assets, whether equities, bonds, a house, a car, whatever.
Yes, banks are lower risk so they offer a lower return. Equities are the reverse although the risk and return varies. If you're sensible, as you say, you keep your savings under the FSCS limit so you reduce the risk of losing money if the bank fails (UK savers lost money in the Icelandic banking crisis).
But you are being rewarded for giving banks the opportunity to make money on lending out a multiple of your money. Take away interest and people would stick their money in government bonds. But you're happy if Janet loses 40% (there was a total bloodbath in bond markets last year) as she's taken the risk. And under normal conditions, you're also happy for her to make 5% for the same reason.
But it's not ok for Dorothy to stick her life savings in a savings account earning 4% as that's low risk. It doesn't matter that the mortgage market would be in crisis as they wouldn't have the deposits to allow them to lend. It's a very odd way of looking at financial markets.