I took quite a minimalist approach. tent, sleeping bag, water bottle, pump, puncture repair kit, camera. ate cold food and pub lunches, camped wild. It was march and I had a -2 degree camp. I only had one set of clothes which I wore the whole trip.
I did it on a cheapo hybrid, but I would be temped by the possibility of doing it in summer on a racer and with just a bivvy bag. or even staying in youth hostels and only taking a water bottle, pump and a puncture repair kit.