Westley was in charge for just over two months, but could only scrape two wins from his nine games in charge to leave the club rock bottom of League Two.
Allen will now undergo his fifth spell as Bees boss in what represents the club's 20th managerial change since 2010. The former West Ham United midfielder's fourth coaching role at Barnet ended in 2016 when he left to take over National League side Eastleigh.
In an interview with Barnet's official club website, chairman Anthony Kleanthous revealed that he should have sacked Westley three months ago.
"Doing nothing was not an option so here we are again, another Monday, another manager. Martin is back. His remit is simple: clear the decks, get everyone focused and win matches. I knew Martin was available and we met for breakfast one morning [in January]," he said.
"I should have given him the job there and then but, at that time I was still thinking we could make the playoffs, and he was trying to convince me we were going to be fighting relegation.
"With hindsight he was right and I was in cuckoo land but, as always when it comes to Barnet, I struggle to accept anything negative and my enthusiasm gets the better of me. I should have listened to him."
Barnet travel to Luton Town next on Saturday, seven points from safety with eight games left to play.