So if you assume it is un-fused spur could you then replace the existing socket with an FCU, add a new socket beside it then extend to the additional sockets.
That way you just have one fused spur, albeit with a limit of 13A on the all the sockets.Yes that is a way of doing it, but spurs in kitchens are really IMO not a good design. About the only place in a modern home you get any type of loading on sockets is in a kitchen, and so having 3/4 double sockets backed by a 13amp fuse is not what I consider a good design. 3/4 sockets on a fused spur in a living room or the like is more acceptable.
It does all assume though that all the appliances are ok with a limit of 13A (ish) and that it is really is a single socket on a un-fused spur to start with.
Do you also need to consider RCD protection? Almost certainly the additional work will need to have RCD protection. whether the OP decides to just RCD protect his work, or the whole circuit is agian his call. I would be trying to protect the whole circuit, could never see the point of have a socket RCD protected and 2 feet away one that wasn't.