I'll soon be travelling with my parents and partner from London to Sydney via Singapore. We have a few hours of layover there. The flights were booked with BA, in First class. All flights are with BA, with the exception of the outbound flight from Singapore -> Sydney, which is with Qantas. Since First was apparently not available on this leg, we we've been booked into business class on the Qantas plane, however the fare type on BA.com is still listed as 'First' for the Qantas flight. When I log in to manage the booking on the Qantas website though, the fare type is not mentioned, but the travel class is 'Business (J)'.

My question is: will we be able to access the Qantas first lounge in Singapore?