There's a peculiar geographic wrinkle worth clearing up before booking anything: Birmingham, Alabama and Glasgow, Scotland are not connected by any nonstop flight, and searching for business class from Birmingham to Glasgow inevitably means routing through a major American gateway and a European hub. In practice, that means Delta, American, or United passengers départing BHM will connect through Atlanta, New York-JFK, or a similar East Coast hub before crossing the Atlantic, since none of these three carriers fly BHM nonstop to any UK point, let alone Glasgow, which itself receives limited long-haul widebody service. Realistically, the most efficient business class routing pairs a domestic first-class connection on Delta, American, or United with a transatlantic business product—Delta One suites on the A330neo or A350, United Polaris on the 767 or 787, or American's Flagship Business on the 777 and 787—landing at London Heathrow or Amsterdam, then finishing with a short intra-UK/European hop into Glasgow.
Having flown this patchwork routing more times than I'd like to admit, my advice is to build in at least a 90-minute connection window at Atlanta or JFK, since BHM's regional jet arrivals can run late during winter storm season, and missing a transatlantic departure gate at ATL's international terminal is a real risk. Delta One's suite with closing door on the A330neo is the standout hard product among these three carriers if your itinerary allows routing through Atlanta or JFK; it's worth building your connections around securing that specific aircraft rather than settling for an older 767 configuration. For the final leg into Glasgow, expect a narrowbody domestic-style cabin from a European gateway—don't expect lie-flat seating on that segment, so treat the long-haul leg as your primary comfort investment.
January through March and October through November consistently offer the softest business class fares on this multi-carrier routing, as both leisure and corporate demand dip outside summer festival season and December holidays. Because pricing and award availability shift constantly across three competing carriers and multiple routing options, setting up fare alerts is the smartest way to catch a premium seat at the right moment rather than checking manually.