Well it appears that was not the end of the story.
Thanks @MikeG - we arrive/depart on EK so will see how it goes!SIN-FRA arrived at Terminal 1. Security was good, and fairly fast, but even with UK passports, you need to go through the non-EU line even if your UK passport has "EUROPEAN UNION" emblazoned on the front cover. We ended up using our Aussie passports...
It took us over an hour to get through security at SYD on the way out, so anything was better than this.
FRA-BHX departed from Terminal 1. The same thing, Security was fairly efficient
LHR-FRA arrived at Terminal 1, but we were just transiting to a FRA-SIN flight so this was super-easy... Especially as when we checked in at the Lufthansa desk at LHR, we were checked in to our connecting Lufthansa ticketed (Separate booking) flights all the way to SYD. There are a lot of good things to say about Lufthansa and Star Alliance.
I hope this helps. The Lufthansa Senator Lounges are pretty good IMHO
One thing that surprised me was that fast-track doesn't apply to guests with Lufthansa - apparently, it's the only airline that does this (according to the fast track lady at LHR).
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Also if the QF F checkin has reopened? (It was still closed a week or so ago)