Can I travel after my citizenship ceremony and before receiving my first British passport?

You can still use your existing non-British passport for travel. However, without your BRP, re-entering the UK might be challenging as this passport does not indicate your right to return to the UK as a citizen, especially if you usually need a visa to enter the UK. Your new Certificate of British Citizenship is not a legal document for entry to the UK.

Travel in an Emergency

In an emergency travel situation where you cannot wait for your British passport, you should carry your naturalisation certificate and any other document that proves your British citizenship. If you are a non-visa national and therefore would typically need a visa in advance to enter the UK as a visitor, you should take your expired Biometric Residence Permit (BRP) with you or at least take a copy of your Indefinite Leave to Remain (ILR) BRP to show to the UK immigration officer if required. It is also recommended that you take a printout of your online e-visa status and generate a share code, which you can provide if necessary. 

However, if you require a visa to enter the UK, it is highly unlikely that the airline will permit you to board the flight, unless they have checked the Home Office system and it shows that you have a current e-visa related to your ILR.  It is currently unclear how quickly the new systems update, which carries a risk.

Please note that despite the above, it's not recommended to travel before you receive your British passport as it goes against official guidance. But if it's an emergency and you must travel, you can do so at your own risk, but be prepared for delays at the airport. It's advisable to consult with a UK immigration specialist who may provide you with a 'comfort letter' to support your entry back to the UK.