He entered the Lords after choosing not to seek re-election to the Commons, where he served as an opposition spokesperson for Scotland and Northern Ireland, as well as a senior whip.

Along with Robert Brown of the Scottish Liberal Democrats, he successfully campaigned for his hometown (an independent royal burgh from the 1100s to the 1970s) to be removed from the district of Glasgow and allocated to South Lanarkshire ahead of local authority re-organisation in 1994, via a local referendum.

An early day motion in July 2006 noted "the difficult task he has of securing government business whilst accommodating the parliamentary, political and personal requirements of 352 Labour colleagues" and congratulated him for "the respect he has earned from all sides of the House for his ability to perform these duties"; it was signed by 135 MPs.

McAvoy was appointed Knight Commander of the Order of the British Empire (KBE) in the 2022 New Year Honours for political and public service.

[9][10] McAvoy and his wife Eleanor were married in 1968 in St Columbkille's Church [de], Rutherglen, and had four sons.

[11] His brother Eddie is a retired local politician who also worked at Hoover and subsequently served as the leader of South Lanarkshire Council from 1999 to 2017.