Indeed, as a UK citizen (without any EU citizenship) he would be limited to the right to live and work in the UK and Ireland, the rest of the EU/EEA would not be possible. There is always a possibility to get an EU blue card, but that requires a university degree and a binding job offer, depending on country the employer would have to prove first that he cannot find another suitably qualified EU local or EU citizen for the job, which is currently and for the next few years impossible for pilots.
The right to live and work is quite independent from the license anyway. One needs to have both.