The phrase "on returning home" is correct and can be used in written English.
Example: On returning home, I realized I had forgotten my keys and had to wait for my roommate to come back and let me in.
You might, one of these days, perhaps on returning home for Christmas, find yourself in one of those Apple Sourz stained dens of iniquity.
But on returning home, he inadvertently left it behind.
Now, on returning home, he says, he was too depressed even to watch TV.
On returning home, she held court in our back yard, visited by friends and family.
But on returning home, he realised that 10 family members had disappeared.
On returning home from school, he would lounge against a nearby tree and watch.
On returning home, he found his wife's body and raised the alarm.
The squad received a heroes' welcome in Budapest's main square on returning home.
But his elderly mother insisted on returning home to the tent in the garden.
In Volume 6 of the "Sword of Truth" fantasy series, Richard is captured on returning home.
Excited on returning home, he posted his findings on soulstrut.com, a digger Web site.
