Here's a fact worth knowing before you book: there is no nonstop path for business class from Jacksonville to Birmingham, and there never will be given the market size on both ends—BHX here refers to Birmingham, UK's smaller international airport, which simply doesn't draw widebody service from the Southeast. Every routing runs through a major East Coast gateway, and after years of flying this corridor, I've settled on funneling through Atlanta on Delta or Charlotte/Philadelphia on American, then transatlantic to London Heathrow before a short domestic hop or train up to Birmingham. United's option through Newark to Heathrow works too, but the JAX-to-Newark connection is tighter and less forgiving if weather rolls through Florida in summer.
The real prize on this itinerary is the transatlantic leg, where Delta's A330-900 or A350 Delta One suites (fully enclosed, direct aisle access) consistently outclass what you'll find on American's 777 or 787 business cabins on this corridor, though American's Flagship Suite on select 777s is a worthy alternative if the schedule aligns better. United typically flies 767s or 787s with Polaris seats out of Newark—reliable, but not the standout. My insider tip: skip flying into Heathrow's Terminal 5 if you're continuing to Birmingham by rail: instead, route through Heathrow's Terminal 3 arrivals with American or Delta, then take the Heathrow Express to Paddington and a direct train to Birmingham International, which often beats the connecting flight's total door-to-door time and spares you a second security screening.
Seasonality matters more than most travelers realize here. January, February, March, October, and November consistently offer the softest business class fares, largely because Birmingham's corporate travel calendar (finance, automotive, and manufacturing conferences) creates fare spikes in spring and early autumn that don't affect these shoulder months. Given how thin the premium cabin allotments are on this specific JAX–BHX combination, I'd strongly recommend setting up fare alerts rather than checking manually—award space and discounted business fares on this routing tend to open and close within narrow windows that are easy to miss otherwise.