If the records below show that John Billington was in Lincolnshire, then he could have earlier been in one of the neighboring counties of Leicestershire, Rutland or Northamptonshire (noting that the Northamptonshire parts near the Billington records apparently became part of Cambridgeshire and were also called part of Peterborough).
In Feb 1650, Francis Newton (probable nephew of Francis Longland) was reportedly in Swayfield (Lincolnshire) which is less than 4 miles north of the county of Rutland, less than 7 miles east of Leicestershire and less than 7 miles northwest of Northamptonshire (or, old Northamptonshire and new Cambridgeshire; or Peterborough).
On 25 Apr 1604, a John Billington, son of John, was christened at the Parish Church of Thurlby in Thurlby-by-Bourne which is less than 4 miles northeast of the county of Rutland, less than 14 miles east of Leicestershire and less than 7 Miles north of Northamptonshire (or, old Northamptonshire and new Cambridgeshire; or Peterborough).
On 24 Jun 1607, a Francis Billington, son of William(?), was christened at Saint Michael, Stamford (Lincolnshire), which is on the border of Rutland, with a corner of Rutland to the west and northwest of Stamford. Less than 15 miles northwest of Stamford is Leicestershire and less than 2 miles east of Stamford is Northamptonshire (or, old Northamptonshire and new Cambridgeshire; or Peterborough).
Stamford is in a “finger” of Lincolnshire, with a corner of Rutland to the west and to the northwest; the City of Peterborough (today Cambridgeshire, earlier Northamptonshire) is to the east of Stamford. As to distances (as shown in Genuki): Stamford Barron (Northamptonshire) is 1 mile east of Stamford and 7 miles southwest of Thurlby-by-Bourne; Bainton is 7 miles south of Thurlby-by-Bourne and 5 miles east of Stamford. In other words, a 3-mile by 3-mile square in this area could have places in Linclonshire, Rutland and Northamptonshire (or Cambridgeshire). Genuki shows the places above in Northamptonshire while Wikipedia shows them in Cambridgeshire.
Some “settlements” in The City of Peterborough are: Ailsworth • Bainton • Barnack • Borough Fen • Bretton • Castor • Deeping Gate • Dogsthorpe • Eastfield • Eastgate • Etton • Eye • Eye Green • Fengate • Fletton • Glinton • Gunthorpe • The Hamptons • Helpston • Longthorpe • Marholm • Maxey • Millfield • Netherton • Newark • Newborough • New England • Northborough • The Ortons • Parnwell • Paston • Peakirk • Ravensthorpe • Southorpe • Stanground • St. Martin's Without • Sutton • Thorney • Thornhaugh • Ufford • Upton • Walton • Wansford • Werrington • West Town • Westwood • Wittering • Woodston • Wothorpe Many if not all of the above were once part of the Soke of Peterborough in Northamptonshire (and many show up in Genuki as being in Northamptonshire, while Wikipedia shows them in Cambridgeshire).
From Wikipedia: “The Soke of Peterborough is an historic area of England that is traditionally associated with the City and Diocese of Peterborough, but considered part of Northamptonshire. It was also described as the Liberty of Peterborough, or Nassaburgh hundred and comprised, besides Peterborough, about 30 parishes. Today the area forms much of the City of Peterborough unitary authority area, in the ceremonial county of Cambridgeshire. The Church of England, however, still describes the diocese as consisting of Northamptonshire, Rutland and the Soke of Peterborough (i.e. the part of the city north of the River Nene).”
Less than 7 miles west of Swayfield, less than 14 miles WSW of Thurlby-by-Bourne, less than 15 miles NW of Stamford andcan be found places in Leicestershire.