The "pukka" way is to remove handles and latch, then chisel out part of the core of the door, and glue in a new section of timber. You do it from the door edge, leaving the faces untouched.
Lots of handles come with through bolts (as mentioned by Ron). You could replace your handles with these. This is probably the easiest way.
TWR is right about the Rawlplugs. I've used that method many times. I usually glue the plugs in as well. It all can be a bit fiddly though ....... and a bit hit & miss. You will need to drill out the holes to the size of the plugs. Use plugs like these.............
http://www.screwfix.c...ed-brown-300pcs/22982
.... the ones that have a "lip" on them to stop the plug from disappearing into the door when you apply pressure.