In my student days (over two decades ago, now), I used to work at a plant nursery in Broom, near Bidford-on-Avon, which was right next to the SMJ trackbed. On one occasion I walked the trackbed from the roadbridge to the River Arrow, just before Broom Junction.
The Railway was an almalgamation of three companies, The East and West Junction Railway from Fenny Compton to Stratford, The Evesham, Redditch and Stratford-upon-Avon Junction Railway from Broom Junction to Stratford, and the Stratford-Upon-Avon, Towcester and Midland Junction Railway from Fenny Compton to Northampton. This site deals mainly with the first two, the third being outside the area covered by this site.
Today, only a small section of this line remains at Fenny Compton, to serve the MoD base there.