No, you wouldn't have access to the Heathrow Clubhouse as this is now restricted to Virgin Gold and Delta Diamond and Platinum travelling on Virgin, Delta or Aeromexico flights. Virgin Gold can use the lounge flying in economy, the others can access it when flying Premium Economy. All other SkyTeam Elites only get access if flying in Upper Class or Delta One.

More details are here on eligibility: https://flywith.virginatlantic.com/g...clubhouse.html
More details here via HfP: https://www.headforpoints.com/2023/0...-access-rules/

For the New York JFK lounge, Sky Team Elite Plus members do have access to that lounge if flying on Virgin, Delta or a Sky Team airline.