The tools I have been required to provide varied a lot. In resent years it has been zero, mainly due to insurance not due to firm being good to me. If a spanner breaks and as a result your injured the company needs to show that spanner was suitable, in the main one does not today break spanners, but be it a bit of metal from a hammer or chisel, or having a crack in the insulation on tools be it meter leads or screw drivers, only when the firm provide them have they got control. So where I work today, I am not permitted to bring my own tools to work.
I have from time to time in different jobs sneaked in my own tools, I find a clamp-on ammeter good to avoid borrowed neutrals, same applies with a neon screwdriver. However any tools you take to work, should be of a type where if faulty it will not put yourself or others in danger.
Around the year 2000 a guy working with me was taken to court and fined because he brought in an extension lead which he left in his locker, and unbeknown to him, some one borrowed it, and it was faulty, crack in insulation, some one got a shock, as standard procedure was taken to hospital who in turn reported it to HSE.
Years ago as an apprentice I had to have spanners up to around 21 mm, above that was down to firm, and screwdrivers, pliers, side cutters, hacksaw (not the blades) and tool bag. General rule was any tool which wears out, or costs more than in today money £20 was provided by firm.
Channel lock pliers (some times called water pump pliers) and moving spanners were frowned upon, some times banned, kept in compartment under main bag so no one would find them. As a maintenance spark no one seemed to worry, but as installation spark you didn't want to mark the gland, so correct spanner every time.
Where the firm did allow you to have your own tools some people went daft, massive tool boxes which doubled as a work bench, and they paid snap-on a silly amount a week to buy it all. It became a problem as these people could do jobs which others could not as they had the tools rather than the company, and also their tool box got into everyone else's way.
In the main you need to carry hand tools with you, including up/down a ladder so even a tool bag like this
may be too big with some jobs, but you should not be buying more tools than you can carry around with you, tool boxes are useless when going up/down ladders so tool bag is way to go. And light enough to carry, when working on the building of T5 although we had a pick-up, the normal way to get around site was walking, you don't want a heavy bag, so in-spite of saying no moving spanner, in real terms you had little option, and since they do wear out, firm provided in the main. Water pump pliers come in a huge range of quality. These
are useless and likely to slip and injure your hands, these
are far less likely to fail. Also cost more.
Asking the right question is often the way forward, so not what tools do I need to buy, but am I permitted under your insurance to bring in my own tools. Often bosses don't think about insurance and what their responsibility is. Even as a volunteer on local heritage railway in Llanfair I am not permitted to use my own hand tools. They should if following rules also provide safety boots and overalls, but since some people only ever do one day, we are asked to provide our own, but that is unofficial, and if some one didn't then managers would select jobs with no danger like buttering bread in kitchen.
If I ever want to be an engine driver, then I have to be reasonable, and often that also applies to paid work, even if they should provide all tools, borrowing the instructors tools is not going to make you popular, so side cutters, pliers, junior hacksaw, moving spanner, channel lock pliers, and screwdrivers and bag shows willing, any other tools you buy as you see they are needed. Likely with bag £50 to £100 for start up tool kit. I would be temped to get something like this
at £38 then replace items with better quality as you find required. It shows you are willing to bend rules to help, without going OTT. But it will depend what you are doing, when working fitting alarms, I bought a cheap battery drill to use as an electric screwdriver, but I was on bonus.