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 (unsuccessfully) for Scunthorpe Town Council.
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 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.
His majority was substantially increased at the 1983 general election, after boundary changes removing the mining area to the neighbouring Sherwood constituency (although that too went Conservative in 1983).
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.