IMO the optimum bike is a hub-geared, disc-braked cross bike with full guards and semi-knobbly tyres.
Realistically, any bike can do it including skinny tyred racers. If the weather is or has been wet then a tourer or hybrid would be better.
While I'm not usually a fan of wearing a rucksack on the bike, it might be worth carying your gear that way because there's a lot of picking up the bike to get it over bike gates. There is also a longish wooden staircase/bridge to be negotiated near Widnes.
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