If you both agree, then you could. However, if you're looking to be able to support more broadly, such as being able to make decisions on their behalf and being able to manage all of their accounts, then you'd need Power of Attorney.
This is a legal document that allows somebody else to manage another's property and finances (and in many cases, health and welfare too) if they were to lose mental capacity. See our full guides to Power of Attorney and Best banks if you've already Power of Attorney.
You can also set up a third-party mandate on one or more accounts with your bank. This allows one or more close family or friends to access select accounts to perform everyday financial tasks on your behalf, such as going in branch, withdrawing money at an ATM and accessing online banking.
See Connected bank accounts for more options.