Her initial goal was to teach dance movement to deaf children, but she began a career in modelling and then began acting in television. Her first screen role was in the BBC series The Queen's Traitor in 1967, in which she played Mary, Queen of Scots. During an interview, thinking Barnet sounded uninteresting, she told a reporter from the Northern Echo she was born in Casablanca, where her favourite Bogart/Bergman film was set.

After many further guest appearances in television series such as The Saint, Callan, and UFO, Beacham's first film roles were in The Games directed by Michael Winner, and Tam Lin directed by Roddy McDowall, both released in 1970. She would work with Winner again in 1971's The Nightcomers, in which she starred opposite Marlon Brando. Beacham appeared nude in one scene, during the filming of which Brando wore Y-fronts and wellington boots under the bed clothes to ensure Winner did not film anything lower than was necessary. Horror would be a genre that Beacham appeared in often during this period, and she was subsequently cast as Jessica Van Helsing in Hammer's Dracula A.D. 1972 alongside Peter Cushing.

Beacham married actor John McEnery in 1973; she became pregnant shortly after the wedding but suffered a miscarriage when she was 3 months pregnant because she fell. Beacham and McEnery seperated in 1979 but stayed married for over another 10 years. They have two daughters, Phoebe (1974) and Chloe (1977).

From 1981–82, Beacham featured as a member of the ensemble cast of the BBC series Tenko, about a group of women prisoners of war held captive by the Japanese after their invasion of Singapore in 1942. Following this, she continued working in theatre and television before landing the lead role in the 13-part ITV drama series Connie (1985). Her roles in Tenko and Connie helped to springboard her into one of her most well-remembered roles, that of the devious matriarch Sable Colby on the television series The Colbys (1985–87). The Colbys was a spin-off of the opulent prime-time soap Dynasty which had been the highest rating programme in the USA that year. Beacham was cast opposite Charlton Heston as the tent-pole couple of the new show. The Colbys never experienced the success of its parent show and was cancelled after two seasons, though in 1988, Beacham was invited to reprise the role of Sable on Dynasty, playing opposite Joan Collins in a season-long "battle of the bitches" scenario.

After Dynasty was cancelled in 1989, Beacham landed the lead role in the children's fantasy film The Wolves of Willoughby Chase, playing an evil governess. She was then cast in the US sitcom Sister Kate, taking the lead role as a nun taking care of children in an orphanage. The series lasted for one season and was cancelled in 1990, though she earned a Golden Globe nomination for the role. She then returned to Britain to play Mrs. Peacock in an ITV game show version of the board game Cluedo (1990). Reuniting with Dynasty Producer Aaron Spelling, Beacham also had a recurring guest role in the popular teen drama Beverly Hills, 90210, playing Iris McKay, the estranged mother of Luke Perry's character Dylan. Beacham appeared in six different television series produced by Spelling, including Dynasty, The Colbys, The Love Boat, Beverly Hills, 90210, Burke's Law, and Charmed. In 1993, Beacham signed on to play Dr. Kristin Westphalen in the NBC science fiction series seaQuest DSV, produced by Steven Spielberg. Her character was the chief Oceanographer and medical Doctor for the submarine seaQuest, however Beacham left the programme after its first season. Throughout the 1990s, she continued to make guest appearances on television programmes, working in both the UK and the US. In 1996, she starred in the BBC drama No Bananas which was set during the war years.

Beacham was involved in launching the Sense-National Deafblind and Rubella Association Fill in the Gaps campaign which aims to give the elderly the support they need to maintain a good quality of life. She also attended the Parliamentary launch of the campaign in June 2006.

In 2003, Beacham returned to the UK to take a role in the ITV prison drama Bad Girls. She played inmate Phyllida "Phyl" Oswyn for four years, partnered with Beverly "Bev" Tull (played by Amanda Barrie) as the "Costa Cons". She remained with the series to the end in 2006. She also appeared in the 2006 movie Love and Other Disasters. She returned to stage work and toured the UK in 2007 as a lead in the Noël Coward play Hay Fever. Later that year, she competed in the 2007 series of the BBC's Strictly Come Dancing with professional partner Vincent Simone, though she was eliminated early in the competition (the second of fourteen celebrities) on 14 October 2007.

On 27 November 2008, it was announced that Beacham had joined the cast of ITV's Coronation Street portraying Martha Fraser, a love interest for Ken Barlow (played by william Roache). She made her first appearance on 26 January 2009 and her last on 4 May 2009.

Beacham was successfully treated for skin cancer in 2009. She had a recurrence of the disease in 2011 but has again recovered.

On 3 January 2010, Beacham entered Channel 4's seventh and final series of Celebrity Big Brother as a housemate; she was the only female to make it to the final and finished in 5th place on 29 January 2010.

In October 2011, Beacham released her autobiography Many Lives in which she discusses her life and career. The book includes a foreword written by her Coronation Street co-star william Roache.

In 2012, Beacham reunited with her Dynasty co-star Joan Collins in a UK television advert for Snickers, however the ad was later re-edited and Beacham's appearance cut. She also appeared as store manager Lorraine Chain in Sky1's supermarket-based sitcom Trollied for eight episodes between August 2012 and October 2012. The same year, she also appeared in three episodes of Sky Living's Mount Pleasant as Aunty Pam.

In January 2013, Beacham was a guest on ITV's daytime chat show Loose Women to promote her appearance on the first episode of the second series of Death in Paradise which aired on 8 January 2013.

In March 2016 Beacham revealed to The Sunday Telegraph that she had been raped, when she had been an up-and-coming Actress, in her twenties.