Robert Kilroy-Silk urged party members to tell the current leader, Roger Knapman, that it was time to go. He has accused Knapman of going back on his promise that he would stand down as leader after the European elections in June.
Knapman, in his defence, said: "I am here to serve. I have done my best for the party and I am happy with my record, the party is still growing. I fully anticipate serving a full four-year term as leader."
Knapman has received the support of Nigel Farage, the UKIP leader of MEPs, who said: "He has been the safe pair of hands. He has been the person with the real political experience and it has worked".
However, Kilroy-Silk responded by saying: "What everybody tells me they want is for the current leader to accept the inevitable and to stand down. That is the only way it can happen.
"We have got a very short period of time between now and the next general election - we need to start now. If we can't start now then we have missed that window of opportunity."
As there is no mechanism for Kilroy-Silk to launch a leadership challenge, he believes now members must act if they want to see he becomes leader before a possible general election next year. He claims that he has support from grassroot members and senior members of the party.