Tony Blair was accused of making the remarks in 1999

Mr Blair was alleged to have used the insult while watching TV coverage of the 1999 Welsh assembly elections, when Labour did worse than expected.

Police also revealed the 10-month investigation had cost �1,656.51.

An inquiry began after complaints about the "insult," which was in a newspaper serialising a former aide's book.

We are grateful for the co-operation of all parties involved in this issue Deputy chief constable Clive Wolfendale

A police spokeswoman said: "Following the publication by the Mail on Sunday of anti-Welsh remarks allegedly made by the prime minister in May 1999, North Wales Police received a number of complaints and decided to conduct a full investigation.

"The Commission for Racial Equality was consulted as part of the investigation.

"North Wales Police and the Crown Prosecution Service have now concluded that there is no realistic prospect of a conviction in this case.

"They have therefore decided not to proceed further with the investigation," she said.

In May, officials declined to comment on claims that police officers visited Downing Street to investigate.

The alleged insult was disclosed by Lance Price in the original version of his book, The Spin Doctor's Diary, serialised in the Mail on Sunday in 2005.

Police apologised to Daily Mail columnist Allison Pearson

The claim was made in a draft version of the book, but was toned down in the final published version to read: "TB f-ing and blinding about the whole thing".

Mr Price said on Tuesday that he gave police a detailed statement "in which I made clear that I was sure the prime minister had never meant any offence to the people of Wales".

He added: "Now eight months later they say there is no realistic prospect of a conviction. This was obvious right from the outset. It would be interesting to know just how much this pointless investigation has cost the taxpayer."

North Wales Police's deputy chief constable Clive Wolfendale said the cost was far less than some commentators had been guessing at.

He told BBC Wales that the investigation had been carried out in a "sensitive and cost effective manner".

Mr Wolfendale said Welsh people were protected under race relations legislation and that there were communities, particularly in the north west of Wales, who were as "isolated, vunerable and threatened" as ethnic communities in major cities. In April, North Wales Police had to apologise to Daily Mail columnist Allison Pearson after accusing her of making "offensive and belittling" comments about Welsh people on the BBC's Question Time programme.

The force received a complaint claiming Miss Pearson had described Welsh people as "little Welshies".

But it later emerged the journalist, who is Welsh, had not appeared on that particular programme.

Officers also investigated remarks made about the Welsh by The Weakest Link quiz show host Anne Robinson in 2001.

The presenter caused outrage in some parts of Wales after calling the Welsh "boring" and "irritating" on the BBC show Room 101.

Police later said four senior officers spent 96 hours looking into her comments, at a cost of about �3,800.