I would strongly recommend that you take at least 2 x 750ml water bottles (preferably 900ml [1000ml are available but don’t fit in a bottle cage very well]).
In ‘normal’ cycling conditions you will need to drink about 500ml (roughly a pint) of liquid every hour. You can double that if it is hot and/or you are working hard. You might feel you can get away with less but you will suffer for it on a long trip (see section on hydration).
So if it is hot, your 2 x 900ml bottles will last you about 2 hours. If you were carrying only 500ml bottles you would need to fill up every hour. Whilst you might be happy to stop every hour there are certain sections of the trip where it may take you longer than that to get between potential safe watering points. And if you are using a major road route, like mine, there are very few watering points because the roads bypass all the towns. So to avoid having to make regular detours you need to make sure you are carrying a reasonable supply of liquids.