Social media influencers Andrew and Tristan Tate lost their bid for release from a Miami jail on Wednesday as they contest extradition to Britain, where they are wanted on rape charges.

In denying bail for the Tate brothers, Miami-based US Magistrate Judge Lauren Louis said the brothers’ wealth and frequent international travel made them “quintessential flight risks”.

“While [the brothers] may not in fact possess what extravagant holdings they portray themselves as possessing online, the record reflects that they possess an exceptional capacity to flee the jurisdiction,” Louis wrote.

In a statement, the Tates’ lawyers said they would “continue to defend themselves against the allegations they face and engage with the appropriate legal processes in each jurisdiction.”

In court filings, their lawyers had previously argued their “extraordinary public visibility” would make it impractical for them to flee, and described social media posts in which the brothers touted their wealth as “theatrical” and “grandiose”.