That's partially right, but the number you're using is wrong.
I forget the exact numbers, but, if you're in your 80's, you have something like a 10% ( or possibly a bit higher ) chance of not seeing out the next 12 months, so it'll be closer to 10% or 20% rather than 60%.
Also, it's not as simple as saying "Your nan was old, so might have died anyway", you're talking averages here. So yes, some COVID related deaths may well not have seen out the year, but you can't tie it down to specific people.
It's also possible that the shielding of 1.5 million vulnerable people will mean that some of that group who might otherwise have died, will now live because they're less likely to be pick up a less serious infection than Coronavirus, which could still have been enough to kill them.