Mr Hough, 53, left his job with Securicor yesterday and did not have another post to go to. He is likely to receive a pay-off of around pounds 280,000 from his two-year rolling contract. Last year he was paid pounds 163,000 including bonuses, with a basic salary of pounds 140,000.
Jeff Pack, Securicor's group treasurer, said: "He went home yesterday and is not coming back to work. His resignation was by mutual agreement. Ed's interest in the business was really more to do with the growth phase."
Securicor said Chris Shirtcliffe, its finance director, would take direct control over Securicor Cellular Services, the mobile phone business in the UK which sells Cellnet airtime. Securicor owns 40 per cent of Cellnet, with the remainder controlled by British Telecom.
Roger Wiggs, Securicor's chief executive, said a further announcement would be made within days about restructuring measures and management changes. Securicor shares fell 11.5p to 264p on the news.
Mr Hough's departure follows long-running troubles with the mobile business, which culminated in the spring with the announcement of an pounds 18m exceptional restructuring charge. It covered write downs on the value of customer contracts in Securicor's accounts because people were leaving the Cellnet network at a much faster rate. The charges contributed to a slump in Securicor's profits in the six months to the end of March, which fell to pounds 19.1m from pounds 47.6m.
Mr Pack said further action would be taken to weed out low-spending customers attracted on to the network by big discounts.
"The economies of service provision have changed dramatically over the past two years. There's been such a degree of bad debt that it's become necessary to be more careful than before."
Though Mr Hough was not in direct control of Cellnet, the mobile operator has also faced a series of fiascos, including the revelation this month of a pounds 40m charge after the company abandoned work on a new billing system. It came on top of a pounds 25m provision to cover billing delays, taken last year, of which pounds 10m was charged to Securicor's first-half profits. In March Howard Ford left Cellnet as managing director.
Jim McCafferty, a telecommunications analyst from ABN Amro Hoare Govett, said Mr Hough's resignation suggested Securicor was determined to get to grips with the division. "They've realised these are loss-making businesses, so reporting direct to the finance director should help their visibility."
Other communications operations in the US controlled by Mr Hough will be the responsibility of Mr Wiggs. Securicor said Bob Shiver, a non- executive director of Intek, its US radio division, would become a full- time chairman and chief executive.