How can I stop this without being perceived as rude?

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

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.

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?

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!

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

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.

Because some people think of others feeling LLFL

Bluebelle I disagree with you. What LLFL (and I) have said is: have a perfectly normal courteous conversation with your brother and just say you want to talk to your mother without him always being there. Where does thinking of others feelings come into it? Nothing is being suggested that could hurt anyone's feelings.

Talk to him first, then ask him to put mum on. He can’t really interrupt then as he’s had his say. If he does you can laugh and say ‘hey you you’ve had your turn. It’s mums go’. If he doesn’t get it then you need to gently speak to him about it. Men don’t get hints. He’ll probably pick her phone up to speak to you if you get her one. It’s the usual male ego thing. Thinking they’re more interesting than anything else.

BlueBelle

Because some people think of others feeling LLFL

I agree. The brother is not thinking about either his sister’s or his mother’s feelings at all. It would be better if your mum had her own phone. Do they have a landline?

I am not suggesting hurting anyone’s feelings! If a woman can’t ask her own brother to back off a bit, then I’m sorry.

It shouldn't be difficult to do, just be direct. As someone upthread says, men don't always do hints etc. Unless of course he's hiding something and is worried what his Mum might say ?

Get her own phone as suggested previously. One with big numbers etc if she needs it.

Also, say to your brother "It is nice to talk to you and hear your news but I also like to do the same with mum. It doesnt work in a 3 way conversation for me so I will ring separately to chat to you. When I ring to speak to mum it is our turn for a chat so please don't interrupt"

If he does interrupt, remind him of the conversation, tell him you will speak to him separately to hear his news and to please not interrupt whilst you talk to Mum.

Good luck

If it were one of my brothers (which it wouldn't be), I'd just say "Bugger off, Bro; I called to talk to Mum."

I doubt they'd take that as rude; they'd probably laugh (and blush!) and then, as requested, bugger off. Nowt like a bit of straight talking where subtlety doesn't get through the level of self-centred gormlessness.

Talk to him first,then ask him if mum can have a chat for a while.

It is actually quite weird and controlling. Is that why you are worried about saying something?

Once mum has her own phone, ask her to phone you when she is on her own, or arrange a regular time when she will be in her own room for your phone call.

Sometimes you just have to face up to the possibility that someone might get offended. That's life.

I don't know where it came from originally, but you can be a lady/be ladylike and be rude occasionally if the definition of a lady is someone who is never rude except on purpose. Go for it, skydancer

Nice definition Baggs gives me hope...

well maybe because it is on his phone, he feels it's really his call. i can see that. and he might want his phone back in order to make a call.
but what is the set up.
whose idea was it for mother to go stay with him.
is she ok with it. how much help does she need. how is her cognition. how much privacy/autonomy does she have there.

Ladyleftfieldlover

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

This made me laugh Ladyleftfieldlover!

Why so cross??

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

Presumably because as the OP is asking for advice, that is not how relationships work in this family!

Well, this week I asked him not to put Mum on speakerphone. He obliged but I could hear her talking to him. So I shouted out Can I speak to Mum on her own as we might want to talk about women's stuff? He immediately rushed off to put the kettle on. We had a couple of minutes to ourselves but then he appeared with the tea and stayed there. I think I'm going to have to be more forceful. For goodness sake, why can't some people take hints. Someone upthread said men always think they're important and this is definitely the case with my brother. He has an inflated view of his importance. Thanks everyone.