My old pull chain 3 speed fan switch has white, purple, blue, grey wires. New switch has markings L (black wire), 1, 2, and 3. How should I connect new switch to old wires?

How were those wires connected to the old switch?

What make is the fan?

Ceiling fan pullchain replacement and repair - Ceiling Fans N More

I pulled the three speed fan switch from my old "box fan" that wasn't working. The switch also had the "L, 1, 2, 3" markings, like your pull chain switch. Mine was a knob type switch that you rotated from Off to High, then to Medium, then to Low. My switch was OK, but the motor was bad. Anyway, in testing the switch, it was arranged so that "L" was "Line" (the HOT power cord wire), 1 was a black wire that gave High fan, 2 was a blue wire for Medium, 3 was a red wire that was for Low fan.
Most likely, as long as the hot wire is connected right, you could connect the other three wires in any order, the only problem being that "Low, Medium, High" might be out of order.