It’s an interesting one, I’m not sure I can answer your question but maybe I can signpost?

It’s not something I can reliably say I have seen come up in many credible places as someone who studies the intersection of intellectual, cultural, and political history in modernish Britain. Strauss more broadly has been incredibly influential in some sectors, but not really for the generational theory per se. I am sure some PhD student must have deployed it as a vehicle at some point, and it could well be common in an area I am not familiar with, but my first instinct is that it is not a common lens…

Crudely, British History, as practiced by British historians (to generalise very very broadly) has a peculiar, at times instinctive, scepticism toward the novel use of conceptual devices of ‘social sciences’ as applied as methodologies/a theoretical lens. It’s a bit passé. Add to this the traditional supreme dominance of social history sourced from a family of marxist-et-al as the means of tends to soak up much of framing of such theoretical options. This is why cultural and intellectual history arrived so late to our shores and remains in tiny isolated insurgencies within particular institutions. While there has been movement in this area since the 70s again this has meant that histories of splinters of cultures etc. have complimented the existing class-focused framing.

Thus there is not huge amounts of space for serious communities of practice to emerge. While it is common to see early career researchers scribbling with so and so at the margins of some journal (lord knows I do it) to explore a well rehearsed field from a novel and hopefully enlightening way, aside from some specific areas (and thinkers who have pierced through this) it is relatively rare to see a discourse form around such intellectual devices.

I would suggest, aside from the obvious library keywords, looking at areas within political/intellectual/cultural debates to see if you can find generational framing of change. While you might not find credible wholesale narratives of change in modern history defined by generations within ‘subplots’ I imagine there is more scope for these, even if they do not use the Strauss-Howe theory. In particular there are some areas where the notable shift in ethos and culture of a group within a broader arc of social and political history over time has caused comment - such transitions may be ripe for the sort of thing you are asking for.

Some off the top of my head include gender, particularly the latter half of the 20th century, the left (particularly trade unions) between the 30s and 80s, family and sexuality through the period, the history of education post Butler (particular the teachers), national identities particularly Scotland and Wales, and the history of policing (both perception and within the police service).

These are only starting points and may well yield nothing, but my gut says you are more likely to find good quarry within the larger debates rather than a framing for said larger debates of change.