'Discussions under way'
A "first meeting" has already taken place between a delegation from Britain's Conservative opposition party and a Lebanese parliamentary committee that included one Hezbollah member, Rammell said.
"We will look to have further discussions and our overriding objective within that is to press Hezbollah to play a more constructive role, particularly to move away from violence," he said.
But he said the change in policy would not pave the way for talks with the Palestinian faction Hamas, saying: "I don't think there's an analogy."
Marwan Bishara, Al Jazeera's senior political analyst, said: "Over the past few months, we've been living in an atmosphere of diplomatic engagement, where behind us was an eight-year period of violence in the Middle East.
"Now that the US, under the Obama administration, is trying to engage with Syria and Iran, it's all too normal that countries like England and France would start talking with parties like Hezbollah, and perhaps in the future with Hamas.
"It's an understanding based on the logic of diplomacy and political engagement and everyone knows this when it comes to the case of Lebanon.
"Now that Lebanon is at the door of elections, Hezbollah has a good chance of winning. Hence, Hezbollah could be part of the governing coalition and Britain is preparing for that".
'Party of God'
Hezbollah, which means "Party of God" in Arabic, was formed after Israeli troops invaded Lebanon in 1982.
In 2006 it fought Israel in a month-long war, but has not since been involved in conflict with its neighbour.
The group has MPs in the Lebanese parliament and a minister in the national unity government, which was formed last year following an accord that saved the country from the brink of civil war.