I take issue with the notion that SCGB is "our national skiers' club". It isn't for me and never will be. To my life as a skier it is a total irrelevance and they don't represent me or any other skier I have ever met.
It the Far South in the remote city of London, some may have convinced themselves that this is a national club but at the centre of the action in the British Isles, the Highlands, SCGB has no bearing at all. Long may it stay that way.
The Ski Club of Great Britain is by far the largest and oldest snow sports club in the United Kingdom. Even in Scotland it has a membership that exceeds the Ski Club of Scotland. It is also doubtful if the Ski Club of Scotland has ever lobbied any member of government on anything. Also like it or not, at the moment Scotland is not a sovereign independent country so the statement by the SCGB is factual and accurate.
I would note that the vast majority of snow sports enthusiasts from whatever part of the United Kingdom you are from are not members of any club. The vast majority of walkers in the countryside are not members of the Ramblers Association for example, but does not stop them representing their interests. The same is true of mountaineering and rock climbing or for that matter any other pastime. I think you need to get over it and accept that the largest and oldest snow sports club does like it or not represent all snow sports users in the United Kingdom.