The branch - which presumably is the stub end of the old inland route to Newton Abbot - now seems to end at the edge of Sainsbury's car park. Presumably the untidy looking area just to the East of the line is/was the scrapyard. Was the supermarket built on the site of a former goods yard?
The scrapyard is Sims Metals Exeter, which is still active (in the Google satellite view, there are some pld wagons on the siding that have presumably been delivered for scrapping).
There was orignally pretty much nothing on either side of the line (the Exeter Railway's connection to the Teign Valley Line) apart from a timber yard and small goods depot at the junction with the main line where the Aldi is today, which had their own sidings (the trackbed is still visible to the wall of the car park). The Marsh Barton greyhound stadium was then built to the east of the line (where the Bristol Street Renault dealer is today) in the 1920s. In 1939 Exeter Corporation built a livestock market to the west of the line at Marsh Barton Lane (where the McDonalds and retail park is now), which also had it's own siding and loading dock, accessed off the timber yard sidings.
After the war the land on both sides of the line was earmarked to become Marsh Barton Trading Estate, which started to be constructed in the early 1950s (the stadium closed in 1957 and the land became part of the estate).
The line was closed and lifted in 1962 with the stub left as Alphington Road siding to service the trading estate. The estate had it's own internal sidings, the alignments can be traced by following the southern and eastern boundary walls of the Sims site. The A377 link road to the A30 junction was built on the former railway embankment.
The Sainsburys was built on the site of a former Ministry of Agriculture storage depot and offices in the late 1990s to replace the superstore that used to be at Exe Bridges.