There's no nonstop path linking Silicon Valley to Yorkshire, so anyone booking business class from San Jose to Leeds needs to think in two legs rather than one: a domestic-to-international connection through a major US gateway, then a short European hop into Leeds Bradford Airport, which has no widebody service of its own. In practice, that means routing through hubs like Chicago O'Hare, New York JFK, or Newark on United, American, or Delta, then transferring onto a partner or codeshare into Manchester or Leeds Bradford, since none of the big three US carriers fly widebody metal directly into LBA. The most comfortable version of this journey puts you in United's Polaris business class on the transatlantic sector — lie-flat seats with direct aisle access on the 777 and 787 fleet — or American's Flagship Suite on select JFK departures, both of which make the ~10-hour transatlantic haul genuinely restful before the final domestic-style connector.
I've found the smartest routing discipline is to fly into Manchester rather than force a connection into Leeds Bradford; MAN has far better long-haul frequency, and the train down to Leeds takes under an hour, often faster door-to-door than waiting on a tight regional connection. If you're connecting through JFK, build in extra buffer time at Terminal 8, since American's international arrivals can bottleneck at immigration during peak summer travel. Delta routes typically funnel through JFK or Boston with a transatlantic partner, and their Delta One suites — fully enclosed on the A330-900 and A350 — are worth seeking out if your itinerary allows for it.
Fare patterns on this corridor favor the shoulder seasons heavily: January, February, March, and again October and November consistently offer the softest business class pricing, as summer demand into the UK from the West Coast pushes fares up considerably. Given the multiple routing options and carrier combinations involved, setting up fare alerts for San Jose to Leeds business class itineraries is the most reliable way to catch these seasonal dips before they disappear.