Should I insulate under my cold water tank?
You shouldn't insulate under the tank (unless the loft is fully insulated on the inside of the roof, with reduced but suitable ventilation - highly unlikely given what you've said.  This is to keep the tank from freezing.
The heat rising from the house is enough to keep the tank from freezing in typical southern UK winters (I'm in Cardiff at the moment, and live in Bristol, so share your climate).
The tank should be insulated - so they got that right at least.  This is typically pretty thin insulation and could be topped up. Uninsulated pipes under the tank aren't a big worry.  That air shouldn't get below freezing.  There's a chance they're overflow pipes, or feed/expansion for a stored hot water system if you have one, both of which are less prone to damage from freezing.  I'd insulate them anyway.
What I would do (have done) is form a skirt of insulation around the tank support, so you can't see underneath it.  This will reduce heat loss from the room underneath, and  protect the tank slightly better by holding the warm air under it.  This is a little tricky on the side nearest the hatch in your photos, but some can be stuffed (not tightly) a little way under the tank shelf.
In colder climates and other systems, trace heat sources can be used to protect plumbing in the loft, but prolonged periods below freezing are very rare for us, and tend to be sunny leading to solar gain and a warmer loft.