Richard Brunstrom had called Wrexham MP Ian "Ned Ludd" Lucas

In a statement, Richard Brunstrom and Clive Wolfendale said they were "indeed sorry" for comments made during The Chief on BBC One Wales last November.

Mr Lucas said the apology ended that matter, but said BBC Wales still had "questions to answer".

BBC Wales said a complaint had been received and was being investigated.

During The Chief Mr Brunstrom discussed a press release by Mr Lucas which attacked the force for recruiting two web designers.

We have written to Mr Lucas in fuller terms expressing our regret for this unfortunate episode Richard Brunstrom and Clive Wolfendale

Talking to Mr Wolfendale, Mr Brunstrom called the MP Ian "Ned Ludd" Lucas.

Ned Ludd gave his name to the Luddites, who protested - often by destroying sewing machines - during the Industrial Revolution against changes which they felt threatened their livelihood.

Since then, Luddite has been used to describe anyone opposed to technological progress.

Also during the programme, Mr Brunstrom discussed the concept of "parachuting politicians into safe seats".

In a statement on Thursday, the officers said: "We apologise to Mr Ian Lucas, MP for our comments about him during the television documentary The Chief.

Ian Lucas has also complained to BBC Wales

"The remarks were disproportionate to a challenge he had made over police expenditure and caused an unnecessary prolongation of the disagreement.

"We would also like to correct any suggestion arising from the programme that Mr Lucas is a political 'parachutist'.

"His commitment to the Wrexham constituency is evidenced both by the local method of his selection and by his contribution to the community before, and since.

"We have written to Mr Lucas in fuller terms expressing our regret for this unfortunate episode. We are indeed sorry."

Mr Lucas said: "I am pleased that they have made this apology and I now regard this to be an end to the matter as regards the officers' conduct.

"The BBC's editorial complaints unit is still looking into the matter with regards to the way BBC Wales handled the programme. I still believe BBC Wales have questions to answer."

A BBC Wales spokesperson said: "We have received a complaint which we are currently investigating.

"However as the investigation is still ongoing, it would be inappropriate to comment at this stage."