Here's the official NHS advice:
https://www.nhs.uk/common-health-questions/accidents-first-aid-and-treatments/what-should-i-keep-in-my-first-aid-kit/
I'm amazed that antiseptic cream is included in that list though, as many health professionals would rather that such creams weren't sold at all. (Their use inhibits to growth of new tissue).
I'm also surprised that cough medicine is included in the list, as elsewhere on the NHS website you can be told that they don't work.
Painkillers are often excluded from the contents of first aid kits too but I see that they appear on that list. (As it's a 'first aid kit', rather than a 'medicine chest', I'd prefer paracetamol over ibuprofen, as elsewhere on the NHS site you'll see the advice that ibuprofen shouldn't be used within 48 hours of incurring an injury).
I see that 'sticky tape' is on that list but I'd want to expand that to include both microporous tape, which is excellent for securing small dressings, and fabric strapping, which is useful for bigger tasks.
As someone who spent a decade in charge of first aid in a secondary school, I'd definitely want to add some Melolin dressings to that list. They're great for burns and useful for grazes:
http://www.stjohnsupplies.co.uk/products/First-aid-consumables/Dressings/Pads/Melolin-dressing-pad-10-x-10cm-pack-of-5
(NB: Make sure that you know which way round to use them. The shiny side is applied to the wound).