Regards to SFP I’m sure that originally the cut-off time for Saturdays was 12pm but now I have read the help text again it implies that it is 4pm:

Order cut-off times

Regardless of the shipping speed selected by the customer, Prime orders must be dispatched on the same day that the order is received, as long as the customer places the order before your cut-off time. By default, all orders received in your system order by 4:00 p.m. local time (in the time zone of your warehouse located furthest east) must be dispatched on the same day. Orders received after this time must be dispatched the next working day.

Operational hours and Delivery Days

Sellers enrolled in SFP in the UK are expected to dispatch packages on the day the order is received until the cut-off time six days per week, Monday to Friday, plus either Saturday or Sunday