For instance, in Scotland, polls have shown a consistent successive trend in that the younger generations tend to support Scottish independence far more strongly than the older ones.
How it'll pan out in other political issues UK-wide, I've no idea. It would be nice to think that younger generations become progressively less hidebound and more liberal (to adopt the US framing of the term, rather than the UK one), but I don't know whether that's uniformly the case. I suspect there may be a drive toward greater pragmatism, rather than the strict old tribal paradigms of left and right, which have each failed people in their own ways over the years.
Although the SNP is usually identified as left of centre - certainly to the left of the traditional major UK political parties - I think the key to the party's appeal has been pragmatism in the here and now allied to the presentation of a positive vision of the future, which Labour has been very slow and resistant to cotton on to up here.
The movement attached to Corbyn (which I hope will survive Corbyn whatever his own political future) could maybe tap into that sort of appeal in the rest of the UK (I doubt many would believe the Scottish Labour Party if it tried to encroach on that ground in Scotland - it has a lot of amends to make, and needs wholesale reform, which isn't going to happen under the current leadership, largely to the right of Corbyn), but the main battleground it needs to address first seems to be intra-party. Unless Labour presents a more united and outward-looking face, I can see the new influx of members quickly becoming disillusioned.