A bit puzzled by your post but perhaps you can clarify and date some dates, even approx. dates would help.
We are assuming Thomas was a widow(lamplighter) as he is noted as bachelor on marriage of John Burl and Ruth Harper in 1891 in Marleybone.
English marriage certificates don't list condition (married, widowed, etc.) of father- is this information on a chuch record?
To trace any ancestors in Ireland you need to know both their religion and where they lived (parish if not actual townland). Co. Cork, if that is the right place, covers a very large area.
Civil registration of births in Ireland started in 1864 so for earlier dates you need church records which is why religion and location are needed.
Have you tried checking English census records to see if Thomas also went to England?
