OK - do you have any other documentary evidence regarding the birthplace of William Searby?
From FreeBMD I can find only two instances of a birth in the name of William Searby being registered in the period January 1840 - December 1841 - both are within Registration Districts covering Lincolnshire - March quarter 1840 in Spilsby, and June quarter 1841 in Horncastle District, although of course there are other forenames registered within the period. This in itself is not conclusive since, unfortunately, it was not obligatory to register a birth until 1870's
Again, from FreeBMD I cannot see any marriage for William Searby anywhere in England or Wales during the period July 1837 to December 1841. Therefore we must assume that William (Senior) married prior to the introduction of Civil Registration on 1 July 1837.
The 1851 census shows two instances of a William Searby having been born in the period 1840 - 1841. Both are in Lincolnshire, and both have a father named George. The 1841 birth year is the son of George and Ann, and was born in Goulceby (in Horncastle Registration District) and living in Huttoft, and the other is the son of George and Elizabeth born in Bolingbroke (in Spilsby Registration District) and living in Chelsea. The 1841 shows George, Elizabeth and William living in Bolingbroke.