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Think it's more likely to be the tube, or where it engages with the movement.
Some googling suggests crown, stem and indeed movement could be had for not much more than 20 quid (parts) however I suspect that i may be unlikely to find anyone who will do it for less than about 60.
I will try and get a quote, but given the watch was only about 120 it might be new watch time (or to give fixing it a go myself).
Perhaps something automatic/solar powered/a bit more expensive which will either last longer (this one has only made about 5 years) or to make fixing/servicing a more attractive proposition. Disposable culture sucks.
Likely cost of getting a crown fixed on an inexpensive but liked (by me) Seiko. Screw thread seems not to be engaging so it pops out and in with little provocation.