UK doesn't have a mind of its own and gradually gives up its stance on any matter under US pressure. Here they also want to please Israel. At the end of the day,none of them have proof that Hezbollah were involved in Bulgaria except for their outcome is based on US & Israel pressure in return for AID.
U.S. says it killed 10 AQAP Islamist militants in four air strikes in Yemen since April 23 (Reuters)
from the article: British push to blacklist Hezbollah hits EU opposition