It depends on many things, such as how isolated or close to civilizational you will be, who else is going, the weather forecast, the type of bike you are taking, and if you will be out of mobile phone reach etc etc.
In general. for the average day outing:
Bike Tool kit;
* Puncture repair (vulcanizing solution, patches, sandpaper)
* Pump
* Selection of the correct size allen keys
* Tyre lever
* Tie-wraps
* Gaffer tape (1m length wrapped round pump)
* Chain tool
* Spare brake pads
* Chain power link
First Aid:
* Bandages
* Antiseptic Cream
* Surgical Tape
* Gause
* Co-Codamol
* Asprin
* Anti-Histamine tablets
* Anti-Diarrhea tablets
* Alcohol Swabs
* Emergency blanket
* Butterfly stitches
* Latex Gloves
* Anything else you think you may need (wet wipes, tissues, cotton buds, eye wash, eye bath etc etc)
Other
* Food for the day (oatcakes / chocolate / cheese)
* Drink for the day (water / lucozade)
* Extra clothing; rain / windproof top / trousers, fleece
* Sunglasses
* Suncream (important!)
* Insect repellent (can get suncream with built in repellent – check Boots)
* Mobile phone
* Money
* Camera
Consider a PLB if you are out of mobile phone coverage, and are solo or in a vulnerable group, or just want to play it safe.