No, because it is an important part of the job that you can be based in any European country. It is of vital interest that the airline can send you to work from other bases, even if only temporarily. That's why Brexit was so bad for British citizens in Europe. If your job was to go to trade shows and visit European customers, you cannot do so anymore without extra work visas, etc.
You are able to work, just not in jobs that require travelling outside your country of residency. If you have residency in Britain, you cannot work in any other country either. Freedom of Movement is only for people with an EU passport.