Taking a position on Virgin Media's executive board, she will replace Paul Richmond, who is stepping down at the end of the month after nearly nine years at the company and its predecessor in UK cable, NTL.
In her new role she will oversee teams responsible for media relations, public affairs and regulation, internal comms and corporate responsibility, reporting to CEO Tom Mockridge.
Trafford has worked for more than two-and-a-half years at ICAP, which was hit with a £54m fine last year for its part in the Libor interest rate-fixing scandal.
She joins the media company as it adapts its brand in the wake of being acquired by Liberty Global last June.
The move made the combined business the largest international cable company in the world, serving 24 million people across 14 countries, and prompted Virgin Media to unveil a new British flag-free logo earlier this month.
Virgin Media head of media relations Gareth Mead said: "2013 was a huge year for Virgin Media; going from a UK standalone upstart, challenging the likes of BT and Sky, to a major part of the world’s largest international cable company. The reputation of cable in this country has been transformed over the past few years and with our incredible network powering the fastest broadband and most advanced TV, the future is exciting."
Trafford left ICAP to go on gardening leave last week, with head of PR Serra Balls now overseeing comms on an interim basis.
During her time at ICAP Trafford handled the fallout from the Libor scandal, in which three of the company’s former traders were charged with several counts of wire fraud.
The fine was a major factor in a 40 per cent fall in pre-tax profits for the first half of 2013 to £40m, though analysts pointed to a stronger underlying picture helped by a £50m cost-cutting plan launched in 2012.
Before this, her career spanned top roles at Lloyds Banking Group and ITV, as well as M:Communications, where she had Virgin Media as a client.
ICAP confirmed Balls' interim role but declined to comment further.