Businessman Mr Cockeram, from Caldy on the Wirral, was elected to the Shropshire seat in 1979, succeeding the long-serving Jasper More.
His downfall came as Margaret Thatcher privatised public utilities and encouraged ordinary members of the public to buy shares in them.
Strict rules were applied governing share applications to ensure big money investors could not snap them all up.
Mr Cockeram was accused of making multiple applications for shares in British Telecom and British Gas.
His shock announcement that he would not stand again was made at the Ludlow constituency annual meeting in April 1987, just weeks before the general election that year. He admitted making two applications for British Gas shares but, as with British Telecom, one of them was for his grandchildren.
Mr Cockeram denied any wrongdoing, saying it was not against the spirit or letter of the law to buy shares for an infant.
A few weeks later the Crown Prosecution Service decided that he had no case to answer, which he considered a vindication.
Before coming to Ludlow he had been MP for Bebington from 1970 to 1974, when he lost the seat to Labour after the constituency boundaries were redrawn.
He had been a Parliamentary Private Secretary to the Minister for Industry and then to the Chancellor of the Exchequer, Anthony Barber.
During the war he volunteered for the army in 1942 and joined the King's Liverpool Regiment, being commissioned the following year. He took part in the Normandy invasion, landing on the afternoon of D-Day on Gold Beach as a 19-year-old Second Lieutenant with the 2nd Battalion of the Gloucestershire Regiment.
During the advance he was wounded by a grenade and flown home. On demobilisation he held the rank of Captain.
Married with four children, Mr Cockeram became chairman of Watson Prickard, his family's tailors and outfitters firm.
He became the youngest chairman of the Liverpool Round Table and was a magistrate in the city from 1959, a director of the TSB, and a director of the Liverpool Building Society.
He won Ludlow in May 1979 by a margin of 8,382 votes, which caused some surprise as it was an increase of over 2,000 votes in the Tory majority.
In the 1983 general election he increased his winning margin again, with a majority of 11,303.