The Agreement, known as the Bermuda I Agreement, between the government of the United Kingdom and the government of the United States relating to Air Services between their respective Territories, and which was entered into in 1946 (70 years ago) by US and UK negotiators in Bermuda, was an early bilateral air transport agreement regulating civil air transportation.
The Bermuda I Agreement established a precedent for the signing of approximately 3,000 other such agreements internationally. The Bermuda I Agreement was replaced, in due course, by the Bermuda II Agreement, which was signed in 1977 and became effective in 1978.
The Bermuda agreements were then replaced in two stages, on 30 March 2008 and 24 June 2010, by the EU-US Open Skies Agreement between the European Union (representing EU member states) and the United States. This was in large part because of a European Court of Justice ruling that determined that bilateral agreements between the US and European member states were in breach of EU law. http://europa.eu/rapid/press-release_IP-02-1609_en.htm
But if the United Kingdom leaves the European Union, it will presumably become necessary for the UK and the US to re-negotiate and execute a fresh agreement.
Hopefully, both countries’ governments will see the good sense of conducting their treaty negotiations somewhere in the middle, so that Bermuda will become be the host venue for the Bermuda III Agreement in due course.
For more background on the Bermuda Agreements, see: https://en.wikipedia.org/wiki/Bermuda_Agreement