As mentioned above, there isn't really much left of the former Basingstoke and Alton Light Railway through the town anymore, as a fair bit of it was lost under the Basingstoke Ring Road development scheme of the 1970s. Originally the line curved off at the Stub you mention (by the water works and allotments) and would have down down to where the Ring Road West is now. The former Thorneycroft Factory is where Morrisons is now and there is a little mention of the factory in the Superstore - including a former crane by the petrol station (not that you'd really notice is though!), and it would have had sidings off the branch.
The line then carried on across what is now the Winchester Road Roundabout, heading in a near straight line towards the Viables roundabout - where a short stretch of track remains), curving through what is now the towns new Police Station and across what is now the M3 out towards Cliddesdon and Beyond to Alton.
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