Scandinavia is different in general than the UK (and the US, and Canada where I'm from) in the sense that marriages function a bit differently. Men and women are a lot more equal. Fathers are more likely to take leave to raise their children. It's nearly always the case that both the man and woman work full time and both participate equally in cooking and other chores (interesting you mention Denmark as half my extended family lives there). There's less focus on gender roles.
So, it makes sense that men and women may be equally likely to suggest counselling and equally likely to feel they are being listened to.
Are the Englishmen you mention in Denmark because that's where their spouse is from?
Yes, they typically have Danish spouses, though I had an American spouse and had the same experience. I terms of sharing domestic tasks, the UK and Denmark seem very similar to me and surveys that survey what is actually dome rather that reported seem to confirm this. I accept that Danish men work fewer hours and Danish women a little more than their UK counterparts.
Where there is a difference in the sex roles is in responsibility, which is more equal in Denmark and more on the man in the UK. The other side of that is Danish women often have more self-confidence. My then Danish girlfriend was with a group of women in England who were discussing how their men were such wimps when they had a minor sniffle, when my ex- said I was rather stoic, she got the stink-eye - she did not share their insecurities.
As for why Danish men would be more likely to suggest counseling, I think you are onto something. However, I suspect if you are a man in Denmark, you genuinely would be correct in thinking the counselor is more likely to listen to you. Also, as the role of emotional anchor less heavily placed on the man (as you suggest), men are more used to be listened to and expect it rather more. I know an Australian man who suggested counseling to his wife and he does seem to (good man though he is) have the 'nice guy' tendency of thinking his feelings and emotional needs are the most important thing for everyone.