My brother and I have just been discussing this after he asked me what he could do to safeguard himself in the light of having all this data potentially seized.
I said "not a lot" save for changing your bank account to make the details they have invalid, as it's not like you're going to change your name, move house or magically change your DoB.
Which led us on to thinking that there needs to be a radical overhaul in the way that bank details are used/stored. Either banks need to make account numbers changable, or more reasonable the old sort code/account number/credit card number systems of old and current need to go. In their place, something like a known public identifier such as email address a la Paypal needs to be instated. That way it doesn't matter if your details are compromised, you just change email address for banking.
Most people have got 2FA to get access to their accounts already, extend that to the instatement of payment option on service providers and retailers (like Verified for Visa, but amped up) and you've already gone a long way to securing things.