Triban headset reassembly
Reassembling a headset without documentation or notes is truly frustrating.
The plastic split ring is likely a compression ring which is jammed between the steering tube the top bearing,  if it looks like this:


Otherwise, it is a seal.
The compression ring does not have to go in easily by hand and is usually driven into its final position when tightening the complete assembly with a star nut bolt.
The rubber washer is likely to be a seal, but where it comes from is impossible to say. First of all, you need to determine if it came from then lower or upper half of the headset. Then you can try to find a position where it makes most sense (i.e. where it can prevent mud from entering the headset).
Good luck!