Welcome LondonLad.!!
Is it your ambition to get to a major airline.? A career in aviation is like a step ladder. Pilots start at the bottom and work up. Sometimes pretty quickly, sometimes not so quickly.
Read those big flight school adds carefully. They usually promise an interview IF (big if) you are accepted as a CFI for their school and complete the required time. Not everyone that completes flight training at their flight school gets an offer to be a CFI at the school.
I have known plenty of pilots that did the CFI time, then went Part 135 flying then went to whatever regional that would take them and then onto a major airline.
Then again, I knew a pilot that got an internal recommendation from his dad and skipped the regionals, but that is rare.
Good luck to you,