National campaigning was suspended by all major parties, except Ukip, in the wake of the atrocity, with the broadcaster announcing plans to shift its Question Time Leaders Special to Monday - just days before the June 8 election.
It is the second time that campaigning has been paused, as parties agreed to put electioneering efforts on hold for three days after the Manchester bombing on May 22.
A number of leader’s interviews with the BBC’s Andrew Neil were postponed during this time, including his clash with Mr Farron.
A BBC spokeswoman said: “The Question Time Leaders Special with Nicola Sturgeon and Tim Farron planned for 5.55pm today will make way for a BBC news special on the London Bridge attack.
“We cannot yet confirm the new scheduling of Question Time, but it will be broadcast tomorrow.”
Theresa May and Jeremy Corbyn have already faced a grilling from the BBC Question Time audience, where Mrs May came under fire over public services while the Labour leader was challenged over his views on security.
Several Sunday morning TV political programmes, which is one of the last opportunities for parties to hammer home their messages ahead of polling day on Thursday, were disrupted by the attack in London Bridge.
The BBC cancelled its pre-election edition of the influential Andrew Marr Show, which had been due to feature election interviews with Mr Farron, Brexit Secretary David Davis and shadow chancellor John McDonnell.
It also cancelled the Sunday Politics, which was going to feature interviews with Lib Dem former deputy prime minister Nick Clegg, Conservative Treasury minister David Gauke and Labour’s Chi Onwurah.
A pre-recorded election set-piece with Ukip and the Green Party will go ahead on Sunday at 10.35pm, as well as a separate programme with Plaid Cymru’s Leanne Wood at 10.35pm on BBC Wales.