Hi Christine,  I have looked at Noah da Costa marriages and Da Costa Noah marriages but could not find a Leah as a bride in any of them. I have found all five of her children, as you said, in the Birth Register of BM 1767-1881.  They are, Esther, 30 May 1800, Isaac, 20 July 1803, Abraham, 23 July 1805, Sarah, 21 March 1813 and Sampson, 10 March 1817.
I still wonder whether Leah may not have been Sephardi and she and Solomon may have been married in an Ashkenazi synagogue. I have looked quickly through the Great Synagogue and the New and Hambro synagogue records but cannot see a marriage for Leah there either.  So there is still the possibility of a Church marriage. It did happen and there is one in my family, of a couple who were certainly Jewish.  I have always thought that maybe the couple's parents forbade the marriage and that was a way they got around the family disapproval.
Sorry I cannot help more.