British Prime Minister Boris Johnson condemned the "vile" racism, which included monkey noises and apparent Nazi salutes, and called for tough action from UEFA.
As temperatures rose his Bulgarian counterpart, Boyko Borisov, urged the country's football union president to quit.
"I urge Borislav Mihaylov to hand in his resignation immediately!" Borisov wrote on Facebook, adding it was "inadmissible that Bulgaria... is associated with racism and xenophobia".
Hours later the Bulgarian Football Union said in a statement Mihaylov had offered his resignation and would hand it to the members of the BFU executive committee on Friday, citing "tension created over the past days, which is detrimental to Bulgarian football".
His resignation came shortly before the BFU's headquarters were raided by special prosecutors and police, although it is not clear if the swoop was related to Mihaylov's resignation or Monday night's abuse of England's black players.
Shortly before UEFA announced it had launched a probe into the behaviour of the Bulgarian fans, its president Ceferin stressed the commitment of European football's governing body to root out the "disease" of racism.
"More broadly, the football family - everyone from administrators to players, coaches and fans - needs to work with governments and NGOs to wage war on the racists and to marginalise their abhorrent views to the fringes of society," he said. Earlier, a spokesman for prime minister Johnson said: "The racism we saw and heard last night was vile and has no place in football or anywhere else. "The England players and management showed tremendous dignity and the prime minister commends the players who were targeted with this despicable abuse for their response."
After several English players suffered racist abuse in a qualifier away to Montenegro in March, England manager Gareth Southgate had prepared his side to follow UEFA's three-step protocol for reporting racist incidents that can lead to matches being abandoned.