Miss Gilmore has a degree in law, and a masters degree in European politics, and formerly worked for Yeovil Liberal Democrat MP David Laws before moving back to Liverpool.

The Daily Post understands she had applied for a similar position in the Liberal Democrat office at Wirral council, but was unsuccessful.

Cllr Eldridge has been highly critical of his Wavertree rival, Mrs Kennedy, for “not declaring she employed her boyfriend at our expense” following revelations her partner, Peter Dowling, worked for her as a researcher.

Cllr Bradley said he had no involvement in the appointment of Miss Gilmore. He added: “We gave them the job description through human resources and they put people forward.

“I did not speak to anyone or recommend her. It was the best person for the job, that’s how you always look at it.”

Cllr Anderson said he believed a full investigation needed to take place, and would be writing to the Standards Board.

Cllr Anderson added: “I’ve been in politics long enough to know you should not believe in million-to-one coincidence and there is clearly a huge issue here that needs resolving with honesty and transparency.

“I sincerely hope that, if something improper is found to have happened, the right people are held to account.”

Angela Blundell, of union Unison, said she was concerned to hear that no-one else appeared to have been given the opportunity to apply for the job.

She added: “In the current economic climate when members are at risk of redundancy, they should be sticking to the procedures that are in place, and if they have not been, we would be concerned.

“We would be equally concerned if procedures put in place to save money were being breached or were not working because agency staff cost more money than taking our own staff on.”

The Daily Post understands the agency was not specifically asked for Miss Gilmore by the council.

A council spokesman confirmed the redeployment pool had been checked but that there was “no-one suitable” available.

The spokesman added: “This appointment was made through one of our usual staffing agencies.

“It was for a limited, fixed period and had to be filled swiftly to cover a secondment.

“Questions have been raised about whether the correct procedures were followed, and we are looking into the circumstances of the appointment before taking a view of this.”