The items below can be found from £6 and are available from most independent bike shops throughout the UK. You may have bought some of these items a while ago, but wear & tear can mean using them can damage the bike e.g. worn allen keys on bolt heads.
Unless your bike rolls on solid rubber tyres ( they are making a comeback ), a pump is essential. A track pump stored in the house makes short work of squishy tyres that have been sitting unused for a few weeks. A small frame mounted pump may never be required, but like insurance, it's better to have & not need than to not have & need.
No point carrying a pump if you don't have a tube to use it on. One tube is usually enough. If you get multiple flats when out, new, more puncture resistant tyres may be worth investing in. Especially in the winter when removing wheels and tyres is more uncomfortable in the cold.
Bicycle insurance is handy if the love of your life is stolen. Cover can include accidents, event cover, replacement bike hire and accessory cover. Prices start around £3 a month.
If your bike has nutted axles ( more likely if it's an ebike ), a multitool with spanners and tyre levers rattles less in a bag than loose tools.
Which leads us onto bags. A mid size saddle bag will hold a tube, multitool, tyre levers, small change, chocolate bar and possibly a mobile phone for emergencies. A pannier bag ( if commuting ) will carry a change of clothes, waterproof jacket and lunch.
For added safety rear view mirrors are often used on touring and commuter bikes. Some are mounted via a wedge inside the bar end and more modern ones can be fitted to the headtube or bars using the supplied rubber straps. Helmet mounted mirrors look unobtrusive but offer little due to the small size.
You may already have warmer clothing for the winter, but have you a neckwarmer? These tubes of material ( similar to a snood) are great for keeping your ears warm on cold mornings or covering your mouth and nose if the wind gets up. They can be shaped into a bandana, balaclava, headband, neck scarf, hair scrunchy , beanie or wristband. Some utilise lighter weight materials for spring , others use fleece or merino wool for chilly days.
Mudguard use will reduce the amount of time spent cleaning you and your bike. Mudguards make any bike look messy , but big muddy streaks up the rear of your shorts look more messy. Popular mudguards for mountain bikes are Crud Catchers, wide enough to accommodate most MTB tyres and easy enough for fitting without tools. Quality German brand SKS make various designs of mudguards suitable for hybrids and road bikes.
And finally the boring bits. Brush sets for de-crudding the bike after a week worth of road use. They come in sizes suitable for cleaning the drive train, wheels and frame. Lubes and oil are another item that will get used more often from December through to March.
If you like all your equipment to match, French brand Zefal make a range of mudguards, pumps, mirrors, bags, lubes, brushes and tyre levers.