As a very novice DIY person I want to build a very simple platform bed,
and am struggling to find any advice online for something so simple.
My ultimate aim is to have a frame with four chunky, square legs
(around 15cm square). Mounted on these would be the 4 pieces of the
outer frame (2 running length, 2 running width).

I built a simple platform for our king size bed using 2x4's, 4x4's for the
legs, and a couple of sheets of 5/8" particle board.

I made my frame smaller than the mattress so it provides a "toe kick" of
sorts. This keeps me from stubbing my toes on the corner posts.

The frame itself is a simple box of 2x4's, setting on edge, and screwed
together with 3" deck screws. I added a 2x4 lengthwise down the middle for
a little extra support.

I made the legs out of 4x4's and cut rabbets in the top so the frame would
be supported by the legs and not by the fasteners. I put one in each
corner, one in the middle of each side, and one right in the middle of
the bed under the center rail.

I just used 3/8" bolts, washers, and nuts to hold everything together. Not
exactly an appearance item, but because the frame is inset from the
mattress, you really can't see the frame anyway.

I then screwed the particle board to the frame, and set the mattress on
top. Very sturdy, and no squeaks in more than 10 years.

Ideally the final construction would be easy to disassemble

When I need to move the platform, I just unscrew the particle board top and
carry the whole frame as a unit. Easy enough...

If you don't need the space under the bed, you could just build a simple
plywood box or two that set right on the floor.

Anthony