The UK Independence Party could face a court challenge after its high command rejected demands for a vote on whether to hold a leadership contest.
Mr Kilroy-Silk has made no secret of his leadership ambitions
Fifty-one branch chairmen who support MEP Robert Kilroy-Silk have called for an emergency general meeting - enough to force the move under party rules.
But the leadership says the motion is invalid as the chairmen need to hold local meetings to support the demands.
Mr Kilroy-Silk's backers meet lawyers on Tuesday about their next step.
'No local backing'
The emergency general meeting would vote on whether to hold a postal ballot of party members on choosing a new leader.
Current leader Roger Knapman has said a recent telephone poll organised by the party showed he had the backing of most party members and that there was little appetite for a contest.
But Mr Kilroy-Silk has condemned the poll as being unfair.
On Tuesday, UKIP spokesperson Quentin Williamson said: "The faction which wants to press Robert Kilroy-Silk forward as potential leader has gathered the signatures of 51 branch chairmen to demand an emergency general meeting of the whole party.
"It was presented to the national executive committee on Monday. But to have an emergency meeting it means all those branches must have had an emergency general meeting to permit their chairman to do so.
"This has not happened in any case."
Calling an emergency meeting requires the support of at least 47 of the 233 branches.
Time for change?
UKIP's Wokingham branch chairman Michael Harvey is among those calling for a leadership vote.
He told BBC News Mr Kilroy-Silk would give the party a better chance in the next general election, which is widely expected next May.
"He has a much higher media profile than our current leaders," argued Mr Harvey.
London Assembly member Damian Hockney said he was meeting lawyers on Tuesday afternoon on behalf of the 51 branch chairmen for advice about the next step forward "bearing in mind the best way forward for the party".
He said he had not been formally told of the executive committee's decision.
But said: "We have to take advice immediately because because if we are going to do something, it has to be done quickly so it does not conflict with the election campaign."
He said the change to the constitution was impossible to enforce as it would take four or five months to call an emergency meeting.
'Policy, not personality'
Mr Hockney said his leadership calls were not about personalities.
Instead, he backed Mr Kilroy-Silk's desire for UKIP to field candidates in every constituency, rather than only fighting selective election battles.
A UKIP official said the constitution change had been approved by a ballot of all members and still allowed an emergency general meeting to be called within six weeks.
He said at least one local emergency meeting had been cancelled because supporters of Mr Kilroy-Silk recognised it was a "waste of time".
And he said the leadership was concentrating on campaigning efforts, with its first election "campaign shop" due to open on Wednesday in the target seat of Thanet South.
Ex-chat show host Mr Kilroy-Silk says UKIP would self-destruct if the leadership expelled him from the party.
He has already resigned from the party's group of MEPs.