Sorry for the delay, but I`ve had a bit of a search in Market Rasen, as I was going through.
The closed down bar is actually at 52 Queen Street, although it looks like an old coaching inn as there is an arch where the horses would have entered the yard. The original supports for the sign are still there, but no sign !!!
I asked 2 ladies in the street if they knew anything about the White Hart, but without success.
I also went to the library and while they had some books on Lincolnshire, even with the librarian`s help , again without success, although she did say there was probably more and better information at Gaisnborough Library.
If I go there before I go to the Archives I`ll look again for you .