Two internationally recognised writers who were barred by Home Secretary Theresa May from visiting Greenwich in the aftermath of soldier Lee Rigby's brutal murder by Islamic extremists have lost a legal bid to challenge her decision.

American nationals Pamela Geller and Robert Spencer - whose views are said to be "regarded by some, perhaps by many, as Islamophobic" - were denied entry to the UK after the minister concluded that their exclusion was "conducive to the public good".

Their attempt to get a judicial review of May's decision was thrown out today by three judges at the Court of Appeal in London, who ruled that the proposed challenge had no prospect of success.

Lord Justice Tomlinson, sitting with Lord Justice Patten and Lord Justice Floyd, said the information upon which the Home Secretary made her decision suggested Ms Geller and Mr Spencer intended to participate in, and to address, a rally planned by the English Defence League (EDL) in Greenwich on June 29 2013 - the date of the annual Armed Forces Day celebration at Woolwich Barracks.

This was "an event which would obviously assume special poignancy, taking place as it would only six weeks after the death of Drummer Rigby", who was murdered by two "Islamist extremist terrorists" on the streets of Woolwich on May 22 2013.

Lord Justice Tomlinson said: "It was the advice of the Metropolitan Police to the Home Secretary that the attendance of the applicants at the EDL event was 'clearly not conducive to the public good' as their presence would be likely to augment the number of people attending in order to oppose the purpose of the rally.

"It was further the advice of the Metropolitan Police that should the applicants be allowed to address the proposed rally 'it would undermine community cohesion and may provoke serious violence'. The task of the police in keeping opposing groups apart would be made more difficult."

It was in those circumstances that the Home Secretary "acceded to representations inviting her to exclude the applicants from the UK".

The judge said Ms Geller and Mr Spencer "are by their own recognition internationally recognised writers and authors".

They are regular public speakers whose views "excite controversy and are regarded by some, perhaps by many, as Islamophobic".

In witness statements, Ms Geller, 56, and Mr Spencer, 47, who deny being Islamophobic, said they had no plans to make any public address during their proposed visit to Britain.

Upholding another tribunal's decision to refuse them permission to apply for judicial review, Lord Justice Tomlinson said they had failed to demonstrate an arguable case which "merits full investigation", and "despite the fact that basic freedoms are engaged there is no compelling reason to permit the matter to go forward to a full hearing".