Thank you for your question.
Your application to the Home Office for naturalisation as a British citizenship allows you to travel out of the UK whilst your application remains pending a decision. It is important to note this provision or exemption does not apply to all types of application and therefore it is essential you get the right advice and assistance before deciding to leave the UK. You should not book your plane ticket.
In terms of the Oath for British naturalisation abroad, this is not permitted as you must be physically present in the UK in order to have your naturalisation ceremony in the UK and give an Oath or affirmation.
