Byrne has offered to buy the 25 per cent stake in Omega from existing investors through his Haverford vehicle for 83p per share or a total £50m.
The board has recommended Byrne’s offer and it has been put to investors, but it was still awaiting the Financial Services Authority’s approval to press ahead.
“HBL has received approval from the UK Financial Services Authority for its proposed acquisition of up to 25% of Omega. Accordingly, condition (b) of the Offer has been fulfilled,” it said in a brief statement.
The approval means shareholders are now free to start submitting their shares, though some may hold out for a rival offer from unlisted Lloyd’s insurer Canopius.
It tabled an informal offer to buy the whole of Omega just a day after Byrne made his bid, matching Byrne’s 83p per share price.
Canopius is now waiting for board approval for its bid, but it is unclear how Omega’s biggest shareholder, Invesco Perpetual, would react.
Neil Woodford, Invesco’s fund manager, has said he would support Byrne’s bid to buy a 25 per cent stake while retaining his 29 per cent holding, but has not indicated whether he would agree to sell out to Canopius at that level.