Travelling during the timeframe between citizenship application approval and Citizenship ceremony

My Naturalisation application is under processing and am expecting an answer by end of September. I have to go to Europe in the beginning of October, I do have a valid Schengen visa. Can i travel during the time between the approval of my citizenship application and the citizenship ceremony date? Can i use my ILR BRP to enter UK during the time between application approval and citizenship ceremony? My understanding is that my ILR BRP is valid until the citizenship ceremony when i actually become the citizen and get the certificate. Please correct me if this is not correct. Here is the extract from Guide AN

In addition, please note that should we grant an application, there is a 90-day period
where you will need to arrange attendance at a citizenship ceremony.
But, outside of these timeframes, there is nothing in the citizenship process that would
prevent you from travelling while your application is being considered.

Free to travel.

You are only british once you have attended your ceremony, not from date of Approval.