That had really stirred the brain cells and I can half remember it and I am not sure if it is the same or a bit different. My dad used to sing something just like that. And umpty tiddly eye doh.Nico, I remember Dad saying the 'Um tiddly um tum....'. Long time ago now!
Nan sang "Ighty tiddly ighty, tittle me under me nighty, Blighty is the place for me. "
There was another song when my dad used to tickle me and I ued to shout (beg him) to stop it, and he sang "storp yer ticklin Jork (Jock) stop you ticklin, tickle ickle icklin stop your ticklin Jock. "