"Could some one kindly explain to me why you need a vessel of 5400 tons to put to sea a gun, a missile silo and a helicopter?"
Biggus - wah shield on! You could put this on a smaller vessel, but time has shown that smaller vessels tend to be more difficult to upgrade through their lives. One of the limitations on current ships (T23s) is that they are at the very upper margins of their design limits, and we are limited on what we can do with them.
More space means its easier to upgrade over their lifespan, cheaper to fit new equipment (no immensely complex refits to plug new capability into, aka Leander mid life updates). It also means more space to add new capability over time to allow the ship to carry out new roles, not forseen at the time of design.
Other considerations include the space allowing for better living conditions, which is a major retention issue - no point having lots of ships if the highly trained, highly educated crew, who could walk outside to a much better paying civvy street job, aren't staying in. We'd just end up with lots of gapped posts, and less effective vessels.