The move follows calls by Nicky Morgan, chair of the House of Commons Treasury Committee, for UK regulators to get answers.
In response to the investigations, Morgan said: "Hundreds of thousands of people in the UK have been affected by the Equifax data breach. The FCA is right to investigate the circumstances surrounding it."
An ICO spokesperson said: "It is a complex and fast-moving case and we are working closely with other UK regulators and our counterparts in Canada and the US."
While the ICO can impose fines of up £500,000 for serious breaches of data protection law, the FCA's powers are far more severe.
In fact the regulator could strip Equifax of its credit referencing licence as well as issue fines of up to an eye-watering 20% of annual revenue. Equifax's 2016 global revenue topped $3bn (£2.27bn), and although exact figures for its UK operation are not detailed, its European arm had sales of $253.6m (£192m).
Having originally said that around 400,000 people in the UK may have had their information compromised following the breach, earlier this month Equifax was forced to fess up that the real number was actually 15.2 million.
It insisted 14.5 million of the records breached would not put people at risk of identity theft, although 694,000 consumers' personal and financial information was under threat.
Patricio Remon, president for Europe at Equifax, said: "Once again, I would like to extend my most sincere apologies to anyone who has been concerned about or impacted by this criminal act. Let me take this opportunity to emphasise that protecting the data of our consumers and clients is always our top priority."