Griffin studied at nursing college with comedian Jo Brand and worked as a psychiatric nurse until 1986, when she became an actress. She currently resides in Swansea.
Griffin has appeared in many plays, television programmes and films both in Wales and throughout the United Kingdom. On television, she has been seen in the cult comedy Satellite City, Wycliffe, Life Force, Holby City, Doctor Who, "Gavin and Stacey", "Coronation Street" and "Getting On". Griffin's film work includes Twin Town, Solomon a Gaenor, Human Traffic, The Machine and Under Milkwood (currently filming).
In 2003, Griffin performed a one-woman show, Caitlin, based on the life of Caitlin Macnamara, wife of Dylan Thomas; the Western Mail praised her "finely-honed and perceptive performance". She reprised the show in 2014 to mark the centenary of Dylan Thomas's birth.
This year Helen starred in and co-wrote the critically acclaimed one woman show 'Who's Afraid of Rachel Roberts" which will play in 2013's "Edinburgh Festival".
In 2005, Griffin won acclaim for her role as Karen in Little White Lies, which she also wrote. Her performance won the Best Actress prize in the 2005 BAFTA Cymru awards, defeating expected favourite Billie Piper (who had been nominated for her role as Rose Tyler in Doctor Who). Griffin herself had become associated with Doctor Who by frequently being used as a stand-in for unavailable actors during read-throughs for other episodes. This led to her casting in the episodes "Rise of the Cybermen" and "The Age of Steel", during production of which she continued to impress the production team to the degree that the script was rewritten so that her character survived for longer than originally planned. In the final episode of "Gavin & Stacey", Griffin appeared as Rita the toll woman. She also appeared as a social worker in "Coronation Street" for 5 episodes and has appeared in all three series of award winning comedy "Getting On". In 2016, she starred in its spin-off series, Going Forward, this time playing a different character.
Griffin's first short play, Killjoy, was written for Theatre West Glamorgan (subsequently renamed Teatr na n'Og) and was first performed in 1993. Two more short plays, The Change and A Generation Arises, were performed in 1994. In 1997, Griffin collaborated with Jo Brand on a short play, Mental, which was based on their shared experiences as psychiatric nurses; the two performed an updated version at the 2003 Edinburgh Festival Fringe. Griffin's first full-length play, Flesh and Blood, which deals with racism in Welsh society, debuted at the Sherman Theatre in Cardiff in 2000, and later moved to the Hampstead Theatre in London. In 2002, Teatr y Byd in Newport debuted another play by Griffin, I Love You Superstar.
Griffin adapted her script for Flesh and Blood into the screenplay for Little White Lies, which was filmed on location in Cardiff and Swansea and premiered in the UK on 10 January 2006.
Griffin has been active in anti-war, anti-racism and feminist causes. During the production of Flesh and Blood, Griffin said, "We cannot afford to have a narrow definition of what it means to be Welsh. If we want to move forward we should be proud of multicultural Wales." In 2003, Griffin protested the Iraq War in Swansea, and identified herself as a spokeswoman for Swansea Coalition Against the War. In 2004, she stood as a candidate for the European Parliament on the slate of the RESPECT Coalition. The party won no seats. In 2006, Griffin was arrested for daubing red paint on the National Museum of Wales as part of a protest against Israel's actions in Lebanon. She was held for ten hours and released with a caution.