Pillings Lock Marina is just south of Loughborough and a 10 minute cab ride to the train station. Sure they could accommodate you.
Your other option is Raynsway Marina just north of Leicester, easy bus ride to Leicester train station.
All the other marinas on that section are on the river which is prone to flooding (the Soar goes up and down like a yo-yo) so to that end I would strongly advise against leaving your boat on the towpath of the river.
If neither of the two options above are viable for you then the only other place I would recommend is Sileby Mill. There is a train station in Sileby and although on the river, the moorings can cope with the rise and fall of the river.