BA would be even more challenging without a UK work permit.
I think Virgin and Ryanair group sponsor; BA I think not. I personally prefer to be in Europe anyway - horrendous tax rates vs. public services in the UK. The pilot market there seems to have gone from absorbing huge numbers of foreigner pilots - to having difficulty attracting anyone to go near it. I would be quite tempted by lovely Vienna, even on a modest net salary. Heard ok things about the general operation there.