I'm not British but have a brother who lives there and adores the ways of the people there. He emigrated from the Us and won't ever live here again.
At least to us, he does hug when leaving or first arriving, but beyond that, not much. When he shows emotion it's usually joking and it's usually after sitting a while with wine.
It always feels like being held at arms length. I notice he is not this way with the GF or child they have, though, but have only seen affection with the GF or lack of stone face when they think they are alone.
Nearly ExH comes from a family who cannot stand emotion. He was taught early to handle his feelings himself and that it isn't good to be social when emotional. It's seen as a failure and someone who isn't competent.
I remember a scene he made between us at a family occasion during R, before I knew it was a trick or false R. He made this scene in front of people and I teared up out of frustration and hurt. I left the room, as is what they want and he simply refused to come with me and keep talking. Not only that, but he turned his back on me as I was in tears and returned to the group of his family members and wouldn't face me. One person in the bunch sought me out and it was a family friend, who Nearly Exh called 'stupid' on the way home. I said " She wasn't stupid, she's become my friend." She was the only one to face me when I cried in their group and simply offered me a needed hug.
I've also seen the sisters do it and seen them just about run when there is emotion or talk about personal things. I don't think it's a gender thing, but I think of it as a culture where a person grew up, maybe, like rules in a house or school, where a person spends a lot of time.
If this is something your WH has always done, I don't see how it would or could change, for it's his norm, then. It's a defense mechanism meant to shut people out and I find at least these are people who don't have a lot of experience in how to handle emotion, though are very well educated, some of them. At least Nearly Exh"s bunch think they are in control with the more they can be stone- faced.
I've found, after 20 years of this stuff, that it's a barrier put up on purpose and cannot be broken down. A lot of time and energy is spent on the façade and what I found is that I had to instead determine my own threshold of tolerance for the pain it was causing me.
My parents went through similar things and it finally drove my mother away, as well. My father was raised during the depression and my mother always talked about his parent's not showing or talking about what they feel, so there's another example.
And yes, we do know women who do this, it's a coping mechanism and one of them even told me for divorce advice, "It's okay to pretend things are good and just smile." My jaw dropped at that, for I don't know how.
Sorry for my long reply, for this is a topic that's been part of my whole life.