There's no such thing as a simple hop from the Mid-South to the West of England, and anyone booking business class from Memphis to Bristol quickly learns this route lives and dies by its connections. There is no nonstop option here—Bristol's regional airport doesn't accommodate widebody transatlantic service, and Memphis, despite its FedEx-fueled cargo importance, isn't a long-haul gateway either. The practical answer, and one worth stating plainly: the most efficient premium routing pairs Delta through Atlanta or JFK onto a transatlantic partner into London, then a short domestic or rail connection down to Bristol, since American and United route through their own East Coast hubs (Philadelphia, Charlotte, or Newark) before crossing the pond. I've flown this itinerary enough times to know that Delta's metal, particularly the A330 or A350 with Delta One suites out of JFK or Atlanta, offers the most consistent hard product for the transatlantic leg, while American's Flagship Suite on the 777 or 787 out of Philadelphia runs a close second.
The insider move here is booking the final London-to-Bristol segment as a separate positioning trip rather than forcing a tight same-day connection—Heathrow to Bristol by train (roughly two hours from Paddington) is often more reliable than a short-hop regional flight, especially with unpredictable UK domestic schedules and Heathrow's notorious immigration queues eating into tight layover windows. If you do connect through Heathrow, build in at least three hours; Terminal 3 and 5 arrivals can be brutal for international-to-domestic transfers.
Seasonally, this itinerary softens nicely in January, February, and March, then again in October and November, when business travel to the UK dips and airlines discount premium cabins to fill seats ahead of summer demand. Given the multi-carrier complexity and the way award and paid fares fluctuate on connecting itineraries like this, setting up automated fare alerts for the Memphis–Bristol corridor is the smartest way to catch a Delta One or Flagship Suite fare before it disappears.