To ask if you think this rule is ridiculous?

Depends on the work environment.
I work in the nhs as a nurse and I've seen my fair share of stupid rules.
We even have a sock colour policy and a manager (an 8a lead nurse) who goes round checking our sock colour.
Our trust is also in the highest level of special measures due to incivility

Introduced into construction industries over 15 years ago. Everyone thought same. But then Incidents and near misses involving Slips trips and falls fell by over 80%

Sounds crazy to me. Surely you're a competent adult who can decide whether it's an appropriate call to take in the wild of a corridor etc.
I work in hospital setting and the number of times a doctor is on the phone while running towards a patient.... Because there is some urgent need/emergency! Sure they get the message and hang up while still running but every second counts

It really depends on the environment you’re working in. If you’re working around heavy machinery, moving vehicles, people moving heavy objects - any danger at all - then I’d say I agree. I would go one further and say you shouldn’t be on your phone at all outside of a safe area.

The world is going mad 🤪

That’s similar to the argument people wheeled out when making phone calls in the car was first banned. At face level it seems over the top, but you only have to see people on their phones in shops and high streets to understand how completely unaware of what’s going on around them people are, and how inconsiderate they can be. So if there is a workplace H&S risk I can see why they might want to enforce this. And if there’s an issue with inconsiderate use of phones then I can see why they want to tackle that too :)

Are you allowed to walk and talk to a person who's physically next to you also walking?

This is why we have laws regarding phone use and driving.

Can’t you just answer the phone at your desk? Do you need to be walking around all day?

Yep, like everyone has said its a safety culture thing. I've worked in energy and nuclear organisations and the safety culture meant you couldn't walk with a coffee with no lid - it was wild!! I do get it though, office accidents (look it up) are surprisingly common and can be bad in terms of injuries etc from just slips, trips and falls. Nobody thinks it'll ever be them but it could be. It's obviously overkill but I bet someone has tripped over whilst on the phone or walked into something, because you can't talk on the phone and be fully aware of your environment. Is it that hard to just tell the person you'll call them back once you're at your desk/in a meeting room..? It isn't a ditch I'd die in tbh (albeit I would find it annoying).

That sounds strange especially if you can stop where you are and take the call.
I get up from my desk and walk around whether I get a call and I’m WFH, it helps get my steps in. And I do similar outside when I’m in the office for the same reasons.
But I have common sense and don’t walk into objects. Other people may need rules to govern their stupidity.

My guess is that someone has walked into someone whilst on the phone -

Because when walking and talking you are both aware of any hazards etc but when on the phone you have no idea of what is going on around the other person?

I know. The justification will be (or should be) that a) when on the phone you're concentrating harder to hear the phone and therefore not paying as much attention to your surroundings (compared to speaking to a person who's physically there) and so more likely to trip and b) if you do trip while holding a phone you only have one hand to grab something/steady yourself.

Really it's ticking a box isn't it 😁

There are times I wish this would be implemented at my work place , 3x this year that I have see ( many many more that I have been told about ) where people are talking or texting walking down a long straight corridor and have walked into / kicked the bright yellow "cleaning in progress " signs we to put out because they are not paying attention.

I was thinking exactly of BP when I read the OP: treat the office as you would a rig - hold onto the handrails when you use the stairs, always have a lid on a hot drink as you carry it, no phones while moving, no running in the hallways!

Absolutely this. They want to prove their safety credentials across the board by being able to say things like "we've gone X days without an incident/near miss" and "steps we've taken in 2025 include introducing this new policy, thus demonstrating our commitment..." blah blah

There's probably being an incident or two where people have crashed into each other, tripped down the stairs and had doors open on to them

So the H&S department have made this a rule in response

Then they will have an organisational H&S policy that applies to the entire business, whether you're office-based or operational.

I worked in tech for an engineering consultancy and desk-based staff had to follow the same guidelines as field engineers at the top of wind turbines.

It felt a bit like overkill at times (my favourite was the one about no open-topped hot drinks containers) but ultimately it's about consistency and keeping people safe, no matter what job they do or where they're located.