If you don't have right to live and work within EU, all doors to you within Europe will be closed. Although there is "high demand" in Europe, no airline will sponsor any kind of work visa for you.
I quoted high demand intentionally as although there are many positions advertised there is still high number of applicants for each position so there is no real big shortage, rather normal
healthy demand with healthy chance to get job.
I have myself European but non-eu passport and I have no chance even to apply for many opened positions, I simply have to look at Asia or Africa for job. Good thing is that in UK you have
strong market with strong demand so you should be fine.