IAG agreed a €1 billion (£840 million) deal for the Spanish carrier in 2019, but this was later halved to €500 million (£420) owing to the effects of the pandemic.
The Competition and Markets Authority (CMA) has now stepped in, Reuters reports, and has set a 19 January 2022 deadline for an initial decision.
The European Commission is also investigating the deal, stating in June it was worried the arrangement could harm competition on dozens of Spanish domestic and international routes.
IAG in January said Air Europa would be acquired by BA stablemate Iberia, and would help the group transform its existing Madrid hub into a rival to Amsterdam, Frankfurt and Paris.
An IAG spokesperson told Reuters: “We will collaborate with the CMA. The London-Madrid route is highly competitive and is already part of the European Commission [investigation] process."
