He is Ukip's fourth leader in a turbulent year marked by infighting which saw the party suffer a dismal general election, gaining just 1.8% of the vote share, down from 12.6% in 2015.
Although he did not name her, his comments appeared to be aimed at defeated leadership hopeful Anne Marie Waters, the controversial Sharia Watch founder who has denounced Islam as "evil".
The leader will be announced at the party conference in Torquay, which, according to reports, Nigel Farage will not be attending.
"We want the right to self-determination", Bolton said, calling for an end to decisions affecting Britain being made in a foreign capital.
"Without being united, we can not lead", he said.
The final candidates hoping to turn the party's fortunes around, and ensure Brexit goes ahead, include MEP Jane Collins, Nuttall's former deputy Peter Whittle, London Assembly Member David Kurten, ex-soldier Henry Bolton, John Rees-Evans and Aidan Powlesland - who (genuinely) wants to mine the asteroid belt for minerals.
It Just Got More Expensive to Build an iPhone
This years model features wireless charging , hence the aluminum uni-body design was abandoned for a more traditional glass back. Despite that, Apple estimates that the iPhone X's battery will last about two hours longer than the iPhone 7 Plus.
The party has riven with tensions since then and some commentators said a party set up to oppose European Union membership had lost its reason to exist, particularly after the charismatic Farage stepped down.
On his personal website, Bolton says he will "resume Nigel Farage's legacy by restoring UKIP's relevance and authority". BBC political correspondent Ben Wright said Mr Bolton would be seen as the continuity candidate.
Asked if he would "ban the burka", Mr Bolton said: "I don't think it's about banning the burka, is it?"
However, he said: "Islam is of concern, the nature of Islam and the practices of the religion are such that they tend to have a more dominating effect in a community where there's a larger Muslim population than the Christian population".
Last year, his wife gave birth to their daughter Victoria on a train that had just pulled into St Pancras Station - his third daughter. But, amid the guff, Roger Helmer, the party's energy spokesman, warned against the "undue and excessive" concern with Islamism during the leadership campaign.
New leader Paul Nuttall left in June after failing to win a parliamentary seat in a general election.