Be realistic
OP, be realistic: there is nothing you can do about it. Right or wrong, the policy will not change. Other schools have the same policy. The country will become a Republic before you manage to overturn this policy. No amount of strongly worded "legal letter" (whatever that means!) is going to change that.
If you like everything else about the school, apply.
If this is one of the many things which don't sit right with you, don't apply.
It's as easy as that.
Take Mossbourne Academy. There was an outcry from hundreds of current and former students and staff about its policies of isolating kids in corridors and shouting at them. There was an inquest. The school confirmed the policies. They basically said: "suck it up, we're not going to change that, and there is nothing you can do about it".
Our great system allows schools to basically abuse and harass kids.
If you think you have any chances of changing a phone policy you don't like, think again.
On the school
The Oratory is very marmite, hate it or love it. How do you feel about everything else?
Out of the gazillion reasons to love or hate the school, I would see this as one of the least important, but to each their own.
I mean, let's not forget that this was the school which had in its admission criteria vague bs like participation to Christian life, which included financial donations to the Church, and that it took a fierce legal battle to rule that illegal. I am not religious but, even if I were, that would certainly put me off, Of course, if instead a socially selective environment is what you want, go for it (the Sutton trust and other studies have repeatedly confirmed that state-funded faith schools tend to be more socially selective).
On the policy
I personally think the policy has its place in a city like London. In Crapford-on-shite kids may need the phone to pay for public transport or to look up the bus timetable at an isolated bus stop. Not so in London.
The rationale can be that, with no phones at all, kids won't use them in the bathrooms, and, outside the school gates, they will be more likely to socialise and less likely to waste time on screens. This may also reduce the potential for inappropriate behaviour on electronic devices.
I get it that not everyone agrees, but at least there is some rationale, it's not pulled out of a dark body cavity.