If you are cycling through Havant on the way to Hayling you can avoid the main roads and follow another old railway line which starts from near the railway station.
It starts across the road from the Eastern end of the car park on the station's south side.
If that confuses you a bit, stand outside the station with the sun in your face and then turn left to the end of the car park. The path is across the road and takes you to the bridge across to Hayling. Bear right after the bridge and you will be on the Hayling Billy track.
You will see an old semaphore railway signal but your path goes the other way.
As an aside there was a tender process to demolish the railway bridge near the semaphore in the 1960s.
No one really wanted the job but the man who won the tender discovered that the fittings of the bridge and line were largely brass rather than steel and made a small fortune as a consequence.
If you did fancy a trip to Pompey there is a small ferry across Langstone Harbour. £4 pp bikes are free.
https://www.haylingferry.net/
There are better pubs and fish and chips in Portsmouth though it is another few miles. And if you are catching a train home more choice. The ferry is about a mile and half from the end of the Billy Track.
If you do catch the ferry look to your right and you will see part of the 1944 Normandy Invasion Mulberry Harbour that never made it to France as it broke before it could be towed there.