I honestly wouldn't bother. If you take that to serious airlines with no other flying on the 737 they won;t be happy just to line train you and be done with it. They'll more than likely need/want to put you through a familiar groundschool/sim course. Therefore you'll not save them any money and you may have been taught the wrong thing in the first place.
A lot of pain for not much gain I would say.
Perhaps focus on a type rating for a turboprop that will be cheaper and definitely get you a job with a UK regional. 2 years later you can look to larger airlines at your leisure.
My 2 cents.
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