I notice when I google Sir Thomas Finlay he is " Sir Thomas Finlay of Bawnboy House, Bawnboy"
I found this list of landowners in County Cavan in the 1870's:
Finlay, Alfred (minor) xxxx Ballyshannon
Finlay, Francis (minor) xxxx Corrville
Finlay, Rev. George Drumcar Dunleer, co. Louth
Finlay, John Brackley House Bawnboy
Finlay, John Kildallon Ardlogher, co. Cavan
Finlay, Maria xxxx xxxx
Finlay, Sir Thos., Bart. [Reps. Of] xxxx Hampstead-road, London
Finlay, Robert xxxx xxxx
http://www.igp-web.com/IGPArchives/ire/cavan/censubs/landowners-cavan-d-h.txtIt might give further clues as to how the Finlays are linked together
I notice the Francis Finlay you mentioned was the owner of Corville as a minor.
Sir Thomas Finlay owned land Hampstead-road, London, given the families long service as politicians, I would say he was knighted for his work.
Have you looked for Sir Thomas on the English Census, maybe 1861,1871, 1881?
He may have married in England?