A thermometer can be handy is a possible fever is an issue.
Throat sweets like strepsils tend to come in hand and we usually had some kind of cold remedy in the one my parents had, TCP always seemed to be in there too!
Antiseptic spray is useful, you can get them in the pound shop, wound washes are more expensive. Cream is also good to put on a wound after it has been cleaned up and any debris washed out (where possible).
I was advised that things like clingfilm can be useful for severe burns as it will cover a wound but not stick to the skin though people generally shouldn't be messing with burns without proper training.
Eyedrops are useful. Especially if you can get ones which don't have a shelf date after opening like individual dropper ones.
We always had indigestion remedies too and medicines for diarrhoea (and the opposite) can be useful to have without leaving the house to get.
Sorry, I'm digressing a little to a home medical kit rather than a first aid kit! Is it for home or out and about like in the car?
I was in charge of first aid in a comprehensive school for a decade. I'd start with Daffy's list and then add Melolin dressings (which are great for burns and abrasions).
I'd also add tweezers (for splinters, etc) and a roll of stretch elastic fabric dressing (which can be great for holding dressings in place or replacing safety pins when making up slings).
If the kit was to be taken outdoors I'd add some sterile water (for cleaning wounds) although an ordinary bottle of supermarket water is actually just as good. (Cotton wool pads can also be useful in cleaning wounds).
For football matches, and anywhere else there could be sprain injuries, I'd like to have a can of Deep Freeze Cold Spray handy.
As well as ordinary sticking plasters, I'd like to see some butterfly closure strip included in the kit (for holding together the sides of wounds which might later need stitching - although prompt and careful use of such closures can often prevent the need for stitching anyway).