Royal Mail have this to say about their guaranteed service:

Next day means next working day (Monday - Friday and does not include saturday delivery without additional payment)

We deliver by 5.30pm the next working day in the following postcode areas:
AB30 - 39, 41 - 45, 51 - 56
HS1, 3 - 9
IV21 - 28, 40 - 49, 51 - 56
KA27, 28
KW1 - 3, 5 - 15
KW16 Stromness Town only
PA20 (0&9)
PA28 - 38, 41 - 49, 76, 77
PH15, 17 - 26, 31 - 40, 49, 50
ZE1

We deliver within two working days by 5.30pm to the following postcodes areas:
HS2
PA60 - 75, 78
ZE2, 3

We deliver within three working days by 5.30pm to the following postcode areas:
KW16 - non Town
KW17
PH30, 41 - 44

Saturday Delivery: 

You can read more on this link: https://www.royalmail.com/sending/uk/special-delivery-guaranteed-1pm#faq-19350056-19350051

Order before 2 PM for same day dispatch for items in stock. Graphskill cannot be held responsible for any delays caused by delivery issues provided we have shipped your order at the required time.