Bedford broke the 10,000 metres record in 1973 and, like the two runners featured in the WCRS advertising campaign, sported a Zapatista moustache and a vest.
Lawyers acting for Bedford are asking for 拢200,000 for what they say is trading on his persona without permission.
The Number, which operates the 118 118 service, has hit back and denied that it modelled its campaign on Bedford, arguing that the look was a widely popular one in the decade, which is best known as the one that fashion forgot.
The Number said it did look at pictures of another runner, also a friend of Bedford's, the American Steve Prefontaine, who was killed in a car crash in 1975. Prefontaine, however, did not have the Zapatista look, instead favouring a much smaller and trimmed moustache.
William Ostrom, a spokesman for The Number, said: "It's ridiculous. His look was not even material to his performance as a runner and it was a widely copied look during the 1970s, used by runners and footballers alike. We looked at pictures of another runner Steve Prefontaine, but the look was truly inspired by The Beatles and Sergeant Pepper."
The WCRS campaign has secured 118 118 around 50% of the market in the battle to succeed BT's 192 service. It saw off competition from rivals such as Conduit's 11 88 88, which spent more on advertising but failed to capture the popular imagination.
It also saw off BT's own replacement service, BT Directories 118 500, which failed to make much of an impact.
The 118 118 campaign has gained widespread word-of-mouth recognition and more column inches, with the Seventies vests worn by the two runners gaining a cult status in the summer as they went on sale in Cancer Research charity stores.
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