Born in Carmarthen, Rogers grew up in nearby Swansea. As a youngster Rogers was a member of the West Glamorgan Youth Theatre Company and Upland Arts, the Swansea Gilbert and Sullivan society. She studied at the Royal Academy of Dramatic Art (RADA) in London, where she was in the same year as Claudia Harrison, graduating in 2000.
Rogers's highest-profile roles to date have been single mother and former drug addict Sheena Williams in Series 7 of the ITV drama Bad Girls (2005) and Chastity Green in the BAFTA-nominated BBC mini-series The Sins alongside Pete Postlethwaite (2000).
On stage, from December 2003 to January 2004, she was in Revelations at the Hampstead Theatre in London. In April and May 2004 she performed as Mary Yellan in Jamaica Inn at the Salisbury Playhouse. She then went into a production of Celestina, which started at the Birmingham Rep Theatre and moved onto the King's Theatre, Edinburgh as part of the Edinburgh International Festival that year before returning to the Rep. In February 2006 she appeared at the Bristol Old Vic as Rosine in The Barber Of Seville. In December of that year she played Milady de Winter in The Three Musketeers at the same venue.
In 2007 she played Wing Governor Helen Stewart in Bad Girls: The Musical in London's West End, a role played (as a non-musical part) in series 1–3 of the television series Bad Girls by Scottish actress Simone Lahbib. Rogers previously appeared in this role in the musical's run at the West Yorkshire Playhouse in 2006.
She performed the role of Celia in As You Like It at the Globe in 2009 and played Lady Macbeth in the same theatre from 23 April to 27 June 2010. Later in 2010 Laura made an appearance on the Doctor Who Christmas 2010 special A Christmas Carol, starring alongside Michael Gambon and Katherine Jenkins. After that, she voiced Ves in The Witcher 2: Assassins of Kings and The Witcher 3: Wild Hunt and also Fringilla Vigo for The Witcher 3: Wild Hunt.
In 2011 Laura began performing in the West End production of The 39 Steps at the Criterion Theatre as Annabella Schmidt, Margaret and Pamela, succeeding well known Wicked actress Dianne Pilkington. In 2014 she played the role of Kay Summersby in the play Pressure, at the Royal Lyceum Theatre, Edinburgh , at the Chichester Festival. and in the touring revival in 2018.
- Price, Karen (1 May 2010). Actress brings new meaning to ‘stage diving’ in Macbeth role, Western Mail (Wales)
- (31 January 2011). The 39 Steps cast change at Criterion Theatre, londontheatre.co.uk
- "The Cast of Pressure". lyceum.org.uk. Royal Lyceum Theatre. Retrieved 22 January 2014.
- "Pressure The Company". cft.org.uk. Chichester Festival Theatre. Retrieved 23 April 2014.