Having joined the Young Conservatives in 1957, Alexander served on their National Advisory Committee in 1961 and fought his first elections in 1962 and 1963, standing for Scunthorpe Town Council. He was elected to Retford Borough Council in 1965 and to Nottinghamshire County Council in 1967, serving until 1974. He was elected to Bassetlaw District Council in 1975, and he was Mayor of Retford in 1977–78. He was a parliamentary candidate for Lincoln in 1966 and again in 1970, but he was not chosen by the right-wing local party to fight the by-election of 1973. The seat was won by the sitting MP, Dick Taverne, each time. At the 1979 general election, Alexander narrowly and unexpectedly beat the popular Labour MP for Newark, Edward Stanley Bishop despite the remaining presence of working mines in the constituency. He adopted a maverick approach in the House of Commons, and was never made a Minister. He was fully in support of the Conservatives on defence issues, describing Tony Benn's approach to the Falklands war as a "prima facie case of treason and sedition" and strongly opposing the "no first use" pledge on nuclear weapons. On other issues he was more moderate, being a member of the Tory Campaign for Homosexual Equality for a time. Alexander could also appear a classic Tory. He faithfully supported Margaret Thatcher, bridled at the poor dress sense of the Labour MP Terry Fields, supported rate capping of left-wing councils, and sought the abolition of Wages Councils which set minimum pay rates. His majority was substantially increased at the 1983 general election, after boundary changes removing the mining area to the neighbouring Sherwood constituency. He also supported the Union of Democratic Mineworkers in the 1984 UK miners' strike, but criticised the 31 pit closures announced by Michael Heseltine in October 1992. He was one of many Conservative MPs to lose their seats in the Labour landslide at the 1997 general election. The victor, Fiona Jones, was convicted of falsifying her election expenses in March 1999, and Alexander was to stand at the resulting by-election, but the conviction was quashed by the Court of Appeal in April 1999 with no need for a by-election. After his time in Parliament, Alexander was subsequently elected to serve as a councillor for the Magnus ward of Newark and Sherwood District Council.
Personal life
He married Valerie Ann Winn in 1966. They had a son and a daughter. He separated from his first wife in 1979 and they were divorced in 1985. He remarried in 1987, to Pat Hanson. Alexander died aged 73 at Beaumond House Community Hospice, Newark-on-Trent, after a short battle with cancer.