Hi Researching Alexanders in Taunton and have not come across a connection with Bailey/Bayley
these are only births I find about this time but can recommend this web site to explore further if you have not already found it
http://www.wsom.org.ukTAUNTON ST. JAMES BAPTISMS 1781 TO 1795
TAUNTON ST. MARY MAGDALENE BAPTISMS 1777 TO 1789
William Bailey John/Elizabeth 25 9 1766 St Mary Magdalene
John Bailey Shoebrooks Ann 25 9 1766 St Mary Magdalene
Charlotte Bailey James/Sarah 9 3 1781 bn 1/3/1781 St James
Mary Ann Bailey James/Sarah 27 4 1783 bn 23/3/1783 St James
Mary Bailey?? James/Sarah 25 11 1784 (very faint) St James
Jane Baily James/Elizabeth 15 1 1784 St Mary Magdalene
William Bailey James/Sarah 19 3 1785 St James
Lucey Bailey James/Sarah 26 12 1786 St James
William Bailey William/Mary 20 4 1794 St James
Best wishes
Steve Alexander