If you put your savings into an ISA account you won’t get get any of it taxed. The amount you can legally put into a cash ISA each year is currently £20,000 dropping to £12,000 next year.
Similarly premium bonds are tax free.
Even with savings which aren’t in tax free accounts you would only pay income tax on any interest exceeding £1000 per year.
My DH gets a good monthly works pension, PIP as he had to retire early through ill health and now gets a full state pension. I get a full state pension and a very small works pension as I drew a lot of it out some years ago. We have a joint bank account and joint savings account and are putting money into the savings to get our flat completely refurbished. Our flat is our own (mortgage paid off) but needs a lot of work. We don't get pension credit. My DH is bothered that if we put too much across into the savings we will be taxed and has a savings limit of £3000 in his mind. We are close to that and worried about putting anymore into that account. All the sites I look at mention pension credit and it's all very confusing. Does anyone know what the limit is?