LGBT Labour has written to the Home Office asking that members of the Kansas-based Westboro Baptist Church be refused entry into the UK.
The church, a tiny sect with around 60 members, often picket funerals in the US.
They claim God is punishing the world because homosexuality is tolerated.
The group said on their website GodHatesFags.com that they would be protesting at a performance of a gay-themed play in Basingstoke on Friday.
In a letter to Immigration Minister Phil Woolas, LGBT Labour co-chair Simon Wright referred to the Home Office decision to ban a Dutch MP who is critical of Islam from entering the UK because he would harm community relations.
“As the government refused entry to the UK to Geert Wilders last week, it is hoped that the same laws can also be used to prevent this family from entering the UK to spread their hated of homosexuality,” said Mr Wright.
At least one Labour and one Tory MP have written to the Home Secretary about the issue. It is highly unlikely that WBC members will try to picket in the UK.
The publicity-hungry group have previously threatened protests in Canada, Australia and Sweden but never turned up.