I've found same amazing mistranscriptions of the name Sleap, so I checked Sleech just in case, but no match.
I hadn't looked before, so I took a look at Blizard's Place in the 1851 census. My Sleap's had moved on by then, but your Lavinia Jones was still there (Chelsea North West enumeration district 18).
Regarding 16 College street, in the 1839 Robson's London and Birmingham - Part 1 the occupiers of "College street Chelsea Common" are listed, at No 16 with the following: Dennis Edw grocer; Sleap F.T. "The Acorn" br hse; Brown Geo, plumber; Davis Jas, shoemaker; Davis Job, toydealer.
In the same 1839 Robson's London and Birmingham - Part 1 directory, in the section with names listed alphabetically F.T. Sleap's address is given as Sleap F.T., Beer retailer, 14 College street, Chelsea.
(I haven't found anything regarding an establishment named "The Acorn" - whether that was at 14 or 16 College street, or elsewhere.)
In the 1841 census College street isn't numbered, but I found the page where James Davis the shoemaker & Job Davis the toydealer are still there, but no sign of Jones, nor Sleap, nor any "The Acorn" in the vicinity.
In the 1851 census that same Job Davis was still in College street, but at no. 17 (Chelsea North West enumeration district 17), but I couldn't see any of the others.
I had a quick loom to see if I could find the marriage or baptisms, for which you are searching - but couldn't find them. Would they have been catholic?
rgds, Barry