I often see in Portsmouth (where many UK warships are based)

That many otherwise impressive looking ships have nothing but a Tiny  4. 5inch gun known as the mod 1. 

Apparently their automated and have been around since the 60s. 

I know guns are considered redundant on ships nowadays but what would be the practical use of such a gun... is it purely for sinking tiny vessels and firing warning shots? 

Post-WW2, 4.5 inch isn't tiny. The 5 inch is fairly common, but most ships mount 3 inchers or less.

Being similar sized to a tank gun does it fire similar HESH or AP rounds? 

smg762 said...

Being similar sized to a tank gun does it fire similar HESH or AP rounds? 

Having a completely different target set, no.

Data on the 4.5" including its ammunition may be found here:

http://www.navweaps.com/Weapons/WNBR_45-55_mk8.php

.

Once upon a time its main use was to fire "window" (chaff) shells out to a reasonable distance, with a back-up of firing warning shots.    AA and land bombardment were also practiced.