@Keitai this is an example of an inexpensive First Kit that you should carry either in the van or in your pull-along tool box (if you have one):
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I have added a number of items to mine to make life a bit easier, I always carry a few ampoules of saline solution (from the chemist, they are really cheap):
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Other things in there include tweezers (for splinters and sometimes stuff in the eye), a selection of waterproof plasters, a pair of nitrile gloves, some burn shields, some alcohol wound cleansers, a stretch bandage, a roll of surgical tape, a can of spray plaster (BTW not allowed in an "official" kit), a CPR shield, some paracetemol (again, deffo not allowed in an "official" kit) and a pair of bandage scissors. It'll cost you about £12 for a travel First Aid kit, under a fiver for the scissors (not always necessary, but the best way I know to cut bandage or plaster on the roll) and a few quid for spray plaster - but you do need to top up the kit religiously when you deplete stuff, and once a year you will need to go through and throw out and replace anmything which is out of date (yes, dressings have a best before date). I keep mine topped up from a bigger kit at home together with another slightly more comprehensive kit I have in the van (which contains additional stuff like an eye patch, more dressings, triangular bandages - for broken/dislocated arms, larger size dressing tape, etc. A former colleague of mine (a Site Manager) also carried some sterile zip bags in his kit - to deal with the odd amputation, but then he's had two of them.
The reason for me having a van kit is because I sometimes act as the site First Aider, and I like to ensure that I have the kit to do the job if someone comes to me with an issue - other than amputations, that is.
I think that every tradesman should carry a basic kit - you never know when you'll need to patch yourself up!