I know of two, one adjacent to the LIF and the other near Winchester.
PS Details for Winchester - Southampton is easy to find
River Itchen – Winchester & Twyford Meads
The free stretch in Winchester runs behind the Mash Tun Pub by Water Lane, from the road bridge downstream to the mill.
Then from the High Street down to Wharf Hill. The free fishing on the Itchen navigation is from Garnier Road, by St Catherine’s Hill. You can also fish a nice pool at Compton Lock at Shawford. Park at Church Lane in Shawford, walk across the water meadows, over the main river, and you’ll reach the Lock.
Twyford Parish Council own the fishing rights on the east bank of that section of the Itchen Navigation that is adjacent to Twyford Meads.
Farm Address: Berry Lane, off Church Lane, Twyford, Winchester, SO21 1NT