//…but I am averse to being told I have to become a customer of a third party before the bank will allow me to access my account,…//
Sorry, Karl, but that is utter nonsense. You already are a “customer of a Third Party” (your internet service provider) if you want to access your account online. Even if you wanted to undertake banking by telephone you would be a customer of your landline provider.
//If I lived exclusively among women, 90% or more of child bearing age, I would still feel no compulsion to be seen to buy sanitary products. I similarly feel absolutely no need to carry on me a mobile phone - 99.9% of the time I basically have no use for it at all.//
Sorry again, Karl, but that argument is specious (a polite term for “ridiculous”). It’s not a question of “fitting in”. I am the last to want to do that but a mobile phone for most people is handy. As mentioned, should you break down whilst out driving, or need to contact people urgently whilst on the move. True, until a few years ago we didn’t have them. But at one time we didn’t have computers, we didn’t have landlines, we didn’t have electricity, we didn’t have gas, we didn’t have cars, we didn’t have anaesthetics and people died of (what are now) the most trivial of ailments.
//I am not opting out of online banking I am objecting to what I see as perhaps the most unhelpful method being chosen, as I said at the outset, rendering my access to that account extremely limited. Some, I know, simply roll over and accept without scrutiny whatever is decided "on high" as "the norm", I am questioning why deliberately choose badly (I find it self-defeating).//
Allowing access to bank accounts online is risky. Banks must mitigate against the risks and as criminals become more sophisticated the banks must take steps to make their systems more resilient. Each chooses to do so in their own way. So the answer for you is simple: change to a bank that has adopted measures which you feel able to comply with. A word of warning though – things change and you may find that, having changed your bank the bank then changes its system, perhaps to one requiring the use of a mobile. Whatever your objections to them they are here to stay and if you want to take advantage of modern developments (such as online banking) you will have to have modern tools. You bought a computer to do so and have to ensure its software is updated to be compatible with your bank's ever-changing systems. It seems you may have to bite the bullet and get a mobile phone because detailing your objections on here will not make the bank change the arrangements it expects its customers to comply with. I have a relative who insists on undertaking all his expenditure in cash. He draws cash from the bank at the beginning of each month and spends the rest of the month going round various places paying his bills and buying goods. He is now finding life is becoming extremely awkward as fewer places accept cash payments for bills. He refuses to adapt and it's causing him unnecessary grief. That's what's really happening to you with this issue and you will find it consumes you to the point of distraction. And I'm sure you can do without that.