Liberal Democrat leader Sir Vince Cable condemned the visit and accused the Turkish leader of having an “unacceptable disregard for liberal, democratic values”.
Sir Vince said: “May’s administration appears to have substituted diplomacy for sycophancy in its pursuit of Brexit.
“By permitting a state visit and audience with the Queen, May and Johnson are essentially rolling out the red carpet for a man with a disregard for human rights, who is responsible for alarming oppression and violence.”
Ahead of the trip, Mr Erdogan said the UK was a “strategic partner and ally” and he wanted to improve trade relations between the two countries.
Mr Erdogan said: “We want to continue our economic relations as the governments of Turkey and the United Kingdom without interruptions after Brexit.”
Mrs May and the Turkish president are set to discuss international issues such as the situation in Cyprus where the two nations act as guarantors.
The Turkish leader will also meet business investors during the visit and speak at the Chatham House think tank.