LHR Clubhouse has separate access rules (copied below).
https://flywith.virginatlantic.com/g...clubhouse.html

No access for Flying Blue Golds at LHR and Flying Blue Plats must be in Prem Economy (VS/DL Biz fares qualify not matter status level). You will have access to other Skyteam lounges on international flights. There is no access to DL Sky Clubs in US when flying domestically (must have itin with international Skyteam flight -- the Caribbean is excluded). Delta also tried to eliminate access to Sky Clubs on international flights to fellow Skyteam Elite Plus members who are flying on Basic Economy/Light fares, but reversed that (but they may bring that back at some point). Delta has had ongoing issues with overcrowding at Sky Clubs (mostly at JFK and ATL) and there can be lines (oops, I mean queues) for entrance.