Sequential UK Bank Of England White £5 Notes

They sound like P-344.
https://en.numista.com/catalogue/note202889.html
I have the thin paper variety with the K.O. Peppiatt signature (P-343).
It is impossible to give you a ballpark figure on what your 2 notes would fetch without any understanding of their condition. The fact that they're consecutively # really won't make much of a difference unless they're both UNC or very close to UNC (AU). Some collectors go for consecutive pairs but they usually need to be high grade ('choice' or 'gems'). Once the note drops a grade (like EF) then the appeal to acquire 1 or 2 of them drops dramatically.

Here's an EF note I found online, like yours, listed on Katz which sold for 81€
https://katzauction.com/lot/581154

I would check the final prices (realized) on ebay or other auction houses to get an idea what your notes might be worth once you've determined the grade (or condition).

Good luck & to the CCF!

Thanks so much for the reply walk2dwater.