Consecutive notes can add a premium.
It's common for some collectors also to collect in pairs, which in turn, forces them to pay more for them.
From my experience, usually if the notes are rarer, the premium can exist. Some early Pre Decimal George V for example, there are only a few known pairs, hence making them one of a kind and therefore extremely desirable.
People who collect star notes or numbered notes, such as million numbers also, may like to have a consecutive pair.
The most I've seen charged extra is around 50% on top for the consecutive premium. In most cases though with common material, no premium exists.
You'll find if you research the famous notes or hoard findings, a lot of the notes were purposely broken up, it makes them easier to liquidate/sell to collectors. Conversely, there are many cases, were collectors have gone out of their way to buy a note and then wait until the others appear on the market, to complete a pair or run.