Most of the island of Portsea is below 5 meters above mean sea level (MSL), and almost all of it is below 8 metres. It would not take much of a sea level rise to seriously affect the city. Also remember that tides can be higher than MSL, particular when there is a spring tide or a low pressure storm surge. Climate breakdown makes extreme weather events like storm surges more likely. (Strictly speaking, elevation is measured from Ordnance Datum Newlyn, which is approximately MSL but fixed in 1921 so it doesn’t vary with sea level rise. MSL has already risen 0.2m over ODN.)
As far as I can tell, the highest natural point (discounting railway embankments, buildings, etc) is just by St Mary’s Church, Fratton, at 8.8m above ODN, from OS Terrain 50 data. However, Wikipedia claims “The highest natural elevation on Portsea Island is the road junction Kingston Cross [in North End], at 21 feet (6.4 m) [above spring high tide].” This seems to be ultimately sourced from the Story of Portsmouth, also quoted in The News. Anyway, this is approximately the same as the St Mary’s location, since each measurement uses a slightly different datum. OS measured Kingston Cross at 8.6m above ODN.
While the UK is at slight risk of tsunami damage, Portsmouth is in a relatively protected position.