I had to replace a disintegrated tubular latch the other day so got a replacement with the correct depth and the same backset then Sod’s Law came into force the hole for the previous latch was 22mm diameter whilst the new latch requires a 26mm hole.
So faced with the prospect of chiselling out the hole to make the fit, I looked at the perennial problem trying to drill out a wider hole when you do not have a centre point.
The solution that worked was to use a step drill to drill out a shoulder wide enough for the latch then using the shoulder as an initial guide use a forstner bit to complete the hole widening.
Richard