Elsewhere in the interview, Mr Rees-Mogg, who is chairman of the influential European Research Group of Conservative backbenchers, hit out at the EU for suggesting Northern Ireland could stay in the customs union after Brexit to avoid border checks on goods coming from the Republic.
He said: "I think they’re the stick in the muds in this and have come up with a solution that is wholly impossible for the United Kingdom to accept, that we should take Northern Ireland out of the United Kingdom.
"Why don’t we suggest to them that the Republic of Ireland comes out of the single market and customs union and accepts our regulations? It’s an equally logical suggestion."
Desperation growing daily
He said: "I think they’re the stick in the muds in this and have come up with a solution that is wholly impossible for the United Kingdom to accept, that we should take Northern Ireland out of the United Kingdom.
"Why don’t we suggest to them that the Republic of Ireland comes out of the single market and customs union and accepts our regulations? It’s an equally logical suggestion."
Desperation growing daily