This is the proper way.
With due respect, I think it may be the way to go for bigger integrated schools, as they have the financial means to do it, but I think the average aeroclub or smaller ATOs can't really sponsor the FI course.
Oxford as far as I know is only offering freelance work.
FTE and L3 (if you choose the Portuguese base) could be two very good options nowadays. I would even lean towards FTE as I think they have a better "pipeline" system if you want to move on to airlines later on. But both seem to have plenty of students and weather is good, so you fly steadily and also enjoy the weather during your time off.
Unfortunately I don't know the conditions they are offering. Remember pay is not everything, as if you can get discounted accomodation, loss of license, increased leave... especially if you look at it as a career or at least as a long term job.