Hello,
I mainly have information about the Jelleys in Coventry.
One branch of the family went to London, following their work in the clock and watch industry.
Although we live just 20 miles from Leicester I don't know of any connections with Jelleys living there.
I don't know of any Scottish connection either.
Some years ago I attended a 'Jelley Day' run by Sheila Jelley who lived near to Amersham. She was devoted to a one name study group and seemed to have all known Jelleys listed, have you come across her?