In the not very good Myles Palmer book MK's old band mate Dave Pask makes the point that teaching was a comparatively well paid job in those days and they could afford to buy decent gear.
That's probably when MK bought his Fender, could it be?
I believe he played the Les Paul Special in the Cafe Racers but he must have got the strat around about that time.
on the famous pic of the first DS gig 26th june 77, it's difficult to see exactly, but appart from the National and the Tele Thinline, we can't see a strat on the stage.
however, we can see the strat on pics from the gig in Tramshed Woolwich, 2nd august, and the demos record at the end of july sounds clearly with a strat.
so he might have bought it at last in july
did he left his teacher job at the end of june ? it makes sense because of summer holidays, he might have kept it until the end of scolary year ?
so the 61 strat would have been his first "personnal gift" after he left his job
https://textes-blog-rock-n-roll.fr/dire-straits-donnait-son-premier-concert-il-y-a-45-ans/