Travel within 2 weeks, not meeting deadline because of wring helpline advice!!

Hi everyone, Sorry for the long post, but this info is required to understand our situation fully. Three weeks ago my partner and I discovered that my partner’s passport needs to be renewed before our travel plans on the 21 of June. We didn’t think much of it, as we haven’t heard about the 10 week waiting time in the news and my partner submitted a standard renewal application. Only about an hour later, I saw the 10 weeks processing times and the option to get the passport quicker through added value services. We immediately called the helpline to make sure that we could change the application to fast track or premium service, and we were Told BY THE OFFICIAL ADVISOR that we need to cancel the application and try to book fast track or premium online. When we couldn’t find a way to cancel the standard application we called again, and a different advisor once again confirmed that we can book fast track and just post a letter to the passport office to cancel the standard one. We were assured having two active applications shouldn’t cause problems with booking the second appointment and the cancellation timeline (apparently up ton6 weeks as we later found out) was never mentioned. Fast forward to yesterday and my partner’s fast track appointment when they were refused service on the basis of having two active applications! The only choose was to post the old passport to the passport office in Peterborough and continue with the standard appointment and maybe try to upgrade it. £150 down the drain because they don’t give refunds and now we’re severely out of time before our trip (2 weeks) Later yesterday I called the helpline again and was told that the letter with the cancellation request has been received! So now the priority is to make sure that the standard application doesn’t get cancelled as well! This advisor was very helpful however, and said she will request an urgent callback for us. Needless to say that no one has called either of us so far. In any case, it seems like our only option so far is to go to the office without an appointment 48 hours prior to our trip, unless we magically manage to get an upgrade which seems highly unlikely. But my main question is, can we show up the day before our flight if the application gets cancelled because of that letter my partner has posted? Can we plead our case in that situation, or will we 100% not get let in? Thank you in advance!