As explained by PO counter staff.
Batteries in original packaging unopened – fine.
Batteries inside equipment – fine.
Loose batteries in an envelope not fine.
Not quite that simple. Counter staff should really have a better understanding of dangerous goods.
Batteries in original packaging – fine if not lithium ion.
Batteries inside equipment – fine if less than 100Wh capacity total or 20Wh/cell
Powerbanks count as individual batteries and cannot go through the mail.
Bear in mind that even in the UK there’s an excellent chance your parcel might end up on an aircraft for a segment of its journey, so Royal Mail has to abide by IATA dangerous goods regulations. CollectPlus only ship by road (AFAIK) so they allow them in their terms and conditions.