Camberwick Jigbits
3 dimensional jigsaw made in 1977 by Kiddicraft Limited.

This was a one-off product,rather than being part of a set.
It has 64 thick card pieces which are colour printed on both sides.And when slotted together they form 12 free-standing 3D characters,including Packet the dog and Mrs Honeyman's baby.
All contained in a smallish box of approximately 10.5" x 7" (27cm x 18cm) that has an integral handle.
Stylistically,the figures remind me a bit of something like Crystal Tipps and Alistair - a series that first appeared 3 years prior to this in 1974.
Either way,it's undeniably colourful.And it's very much a dual purpose "play and display" item  ie.plenty of play opportunities for the kids and quite funky little items for adults to display somewhere.
Maybe a P.C.Mcgarry for the desk of the policeman in your life ?
The only other tv spin-off "Jigbit" set I know about is for The Magic Roundabout.

But I've also managed to find 2 more that aren't tv-related -below.
Because whilst this site is obviously for Trumptonalia,this particular page seems to be the "go to" one for any "Jigbits" search.So it seems only fair to try and spread the net a little wider and make people's visit a bit more rewarding.
And if you know of any others then please let me know. (email on home page)