Single glazed are easy enough, you just get a glazier to cut the hole in the glass and buy a special cat flap designed for glass windows. I've never had it done in a double-glazed door, so don't know how easy it would be.
Hi. It's worth calling around local glaziers. We had a new sealed unit made with the cat flap within it (just a standard cat flap from pets at home) by a local firm of glaziers who measured up the unit, took away the cat flap and then made the new unit within a week - it cost around £70 (this was for a half door panel).
We had a cat flap put into our double glazed French Window doors - done by a local firm. Was a floor to ceiling door, so cost around £100 if I remember correctly. They did ask if we wanted to keep the old piece of glass in case we wanted to replace it at a later date, but we're a family of cat lovers and can't imagine living without a moggy, so we declined!
I had one put into a double glazed patio door. A new double glazed pane has to be made and the cost depends on the size of the pane to be replaced. Mine cost £350, but it was an enormous pane. A door pane shouldn't be too much
We had the same as thecatneuter, new double glazed pane in patio door. Cost of new pane with cat flap (edge is sealed so now flap can be put in later no probs) and fitting was £250. We also got to keep old pane so can put back in when we sell the house if needed
My experience was like Dinky's, although more expensive as it was textured glass. I didn't want to replace it with a solid panel as I didn't want to lose the light. So they measured up and brought a whole replacement panel round with a hole in it for the cat flap to go through. Ds had great fun sticking his head through the hole in the door before the guy put the cat flap in!
If you're in or near Leeds, I think Bramley Glass did mine.