Don't assume that Junior necessarily means that his father was also Thomas. I've seen cases where the relationship was grandfather/grandson, uncle/nephew and one last week where there was no relationship at all. It just differentiated two people of the same name in the same parish, one of whom was older than the other.
The GRO only deals with civil registrations which started in 1837, so events in the 1780s won't be found there. You need to be looking in parish registers.
According to the NBI a Thomas Willis aged 77 was buried at St George's Toddington, on 26 Apr 1848. Is this a separate Thomas to the one who died in 1846?
(later: I suspect the 1848 burial was actually Thomas Willison, whose death appears on freebmd in the June quarter 1848 - there's a 73 year old ag lab in Toddington in 1841 whose surname has been transcribed as William, but which looks more like Willison to me) He/they should appear in the 1841 census. There's only one -
Dunstable St., Toddington
Thomas Willis 61 Farmer
Alice Willis 60
Joseph Willis 25
Mary Ann Willis 20
Ruth Willis 4
All born in Bedfordshire
So on the face of it Thomas was born in Beds, although the 1841 is not particularly reliable on this score.
Virtually all of Beds parish registers pre 1813 have been extracted onto the IGI at
www.familysearch.org, making Beds a fairly easy county to research. Alice SNU doesn't look to be an English name. There's an extracted entry on the IGI of a marriage on 6 Jan 1803 at Toddington of Thomas Willis and Alice BAILEY, and another on 26 Aug 1816 at Toddington of Thomas Willis and Alice ROBARTS. You need to view the microfilm to check them both out, to see if in the later marriage Thomas was described as widower, and to see if a parish of residence other than Toddington is given, and to see if the witnesses provide a clue. I can't see a burial of an Alice in Toddington 1803-16.
If the family was non-conformist they may not have baptised their children in the established church, and if they were Baptists they didn't believe in baptising children, so it may be difficult to trace Thomas' baptism from which you would have got his parents' names. But baptists still had to marry in the established church if they wanted a legal marriage. The 1803 marriage is the first Willis entry in Toddington, so it's difficult to know where the father was from. The first Willis burial in the parish church was on 25 Dec 1837 with Susan Willis aged 69. She seems too young to have been Thomas' mother
I would check with Bedford and Luton Archives and Records Service to see if they hold any wills for Willis in Toddington - see
http://blars.adlibsoft.com/wwwopac.exe?DATABASE=catalo%3Earchives&LANGUAGE=0&DEBUG=0&BRIEFADAPL=../web/adapls/wwwreq&DETAILADAPL=../web/adapls/wwwreq&%250=400038953&LIMIT=50 for an extract of the 1846 will of Thomas. He seemed to own quite a bit of property in various places. But it's his father's will you really need. See also
http://blars.adlibsoft.com/wwwopac.exe?DATABASE=catalo%3Earchives&LANGUAGE=0&DEBUG=0&BRIEFADAPL=../web/adapls/wwwreq&DETAILADAPL=../web/adapls/wwwreq&%250=400039212&LIMIT=50You also need to go through the BLARS online catalogue at
http://blars.adlibsoft.com/ and also the A2A archive at
http://www.nationalarchives.gov.uk/a2a/advanced-search.aspx?tab=1There were also numerous Willisons in Toddington at the crucial time
A licence was issued on 9 Apr 1804 for a dwelling house in Toddington in the occupation of Henry Saunders, next to the house of Mrs Alice Wheeler, to be used as a chapel/meeting house. The persons registering the building were Henry Saunders, T.Willis, Alice Willis, James Bailey, Mary Saunders, Thomas Saunders, John Lee
David