score:9
British citizens are allowed to enter and leave the UK on any passport they choose (as long as they can establish a right to enter of course).
There is a question as to whether Bermuda will allow you in on a UK emergency travel document, or on your Brazilian passport. Presumably you somehow got back from Canada to Bermuda without a UK passport, so the same approach should work coming from the UK.
Upvote:2
I believe it is a non-issue. Arrive early at the airport to give any exit immigration checks time to do their thing. You might find there are no checks in which case, bring a book. Bring all evidence that you have that you lost your UK passport and that a new one is in the works as it will help support any Q&A you go thru (if you go thru at all).
The Bermuda Government website has an FAQ that explicitly says you can pick up a 180 day visa on arrival. The passport will allow you to identify yourself to a Bermudan immigration official and your Bermudan residents card allows you to stay. http://www.gov.bm.knowledgebase.co/article/as-a-brazilian-citizen-do-i-need-a-tourist-visa-for-a-5-days-stay-in-bermuda-998.html
From this point forward, until you get your UK passport replaced, travel on your Brazilian passport.
Best of luck!