The ice-cream flavour's packaging has also been redesigned and now features a male couple standing on top of a wedding cake.
The brand has partnered with Stonewall, the charity that campaigns and lobbies for the rights of gay, lesbian and bisexual people.
This week the UK Government is set to open its consultation on how to implement the legislation that will give equal marriage rights to gay people.
Ben & Jerry's has also launched a Facebook app to encourage consumers to use the #applyeverafter hashtag on Twitter and send in their support for the legislation.
A dedicated part of Ben & Jerry's UK site, http://www.benjerry.co.uk/our-values/appleyeverafter, displays information about why the brand has changed the name of its apple flavour, a link to the Facebook app and a drafted letter that consumers can use to send to their local MP.
Ben & Jerry's said it has been an advocate for equal rights, regardless of sexual orientation, since the brand was created.
It ran similar activity in America to celebrate the introduction of gay marriage legislation in the brand's home state of Vermont and renamed its "Chubby Hubby" ice-cream to "Hubby Hubby".
Laura Doughty, deputy chief executive, Stonewall, said: "We're truly moved by Ben and Jerry's support for same-sex marriage in Britain. All people want is to call their long-term relationship by the same name as everyone else.
"Our strong advice to those who disapprove of same-sex marriage is just not to get married to some-one of the same sex".
Follow Loulla-Mae Eleftheriou-Smith on Twitter @LoullaMae_ES