Major Diameter for M10 x 1.50 should be approx 10mm minus a fraction of a mm. That's not technically correct I know but it will do for this example.
Tap drill size for a M12 x 1.25 bore is 10.80mm.
Theoretically you should have 0.80mm before the valleys from the old thread started to interfere with the peaks from new threads. You should be able to drill out old threads with a 10.80mm drill bit clearing all M10 threads, then run your M12x 1.25 tap. However, it's late for me and I may not be thinking clearly. Bed time.