How can I stop this without being perceived as rude?

Because some people think of others feeling LLFL

Tell him you want to talk about “women’s stuff”. Most men run a mile. However she does need her own phone which you could fund on, for example Giffgaff for £5 a month. You can check usage and be warned if running out of talktime. Free calls to other Giffgaff users.
You must be missing one another - which could be the opening gambit for wanting a private conversation. Good luck.

For Pete’s sake just tell him you want a private chat with your mum! Why is that so difficult ?

It maybe doesn't occur to him that he is being rude! You could have a conversation with him right away if it's his phone and then firmly tell him it's mum's turn. If he interrupts tell him he's had his turn. But probably getting your mum a phone would be better - if she would use it!

Second for buying a mobile phone for your mother. Seems a little odd he isn’t giving her any personal space, are you otherwise happy with this arrangement of her living with your brother?

I am sorry, but in your position, the idea of whether I was being rude or not, wouldn't occur.

If I was you I would just tell my brother, politely and firmly that, when I rang my mother, I want to be able to speak to her for as long as we both wished and that we cannot do that when there is someone lurking in the background ready to join in at any moment.

I would also do as others recommend and buy her a mobile phone. There are some with limited facilities and big clear buttons designed to be easy to use by older people. www.doro.com/en-gb/products/mobile-phones/ This is one company that does them, there are others. Show her how and where to charge it, in case your brother tries to control her use by making a big song and dance about charging.

But just saying what must be said clearly and politely is really the only way forward.

Buy a phone for your Mum to use.
It's not a good arrangement at the moment for either of them.