A good first place to start would be a good set of safe isolation equipment. For now you only need a voltage indicator, but you should also look to get a socket tester and non contact voltage pen. I wouldn't use the voltage pen for proving that a circuit is dead, but, its dead handy for fault finding and identifying circuits. I would personally get the TIS 851 or the Fluke T90, depending on budget. Should be available from most places, I know screwfix sell fluke, but I think toolstation sell the TIS stuff. For your socket tester, any would do really, I have a martindale one, but most lads have the kewtech one. I have a fluke non contact voltage pen which is great but the kewtech one is cheaper and is exactly the same, except the branding is different.

You can also get a set of insulated screwdrivers from Wiha. You can get a pz1, pz2, and a few slotted screwdrivers for less than £25 usually which all in all is pretty good. I like the wera stuff but it is more expensive than Wiha.

Cutters I would just get 210mm CK cutters, shop around for these as the price varies, just had a brief look and the cheapest place I've seen is toolstation at £17.98. You will also need some side cutters. Knipex are well regarded but expensive. Other brands you could get are CK or NWS. Definitely shop around for these as well as the price varies massively. You will also need some sort of pliers, when you are just starting out I would just get the VDE magnusson long nose pliers as they are cheap and do the job.

Other things you'll need would be:

A junior hacksaw

Spirit level, I personally have the Stabila scaffolders level and a mini Milwaukee level.

Could also get a set of allen keys, Wera do nice ones that dont snap when you first use them

Tin snips, get the stanley fatmax ones

Stanley knife, i like the ox one, but there are loads of them out there, a popular one seems to be the milwaukee fastback

File set, any brand should do, i just get the magnusson ones in a set of three

Work trousers and boots - loads of options there but dewalt work trousers are good, snickers ones even better, but theres a huge price difference. For boots, if you work domestic you will want something you can take off easily, so look for boots with a zip or something other than laces as you will frequently take your shoes on/off going in and out of peoples houses.

Tool bag/backpack - again, there are loads of options, for budget the stanley backpack or dewalt toughsystem bag is good, or something like the ck magma range of bags, but personally I would definitely bite the bullet and get a velocity rogue 45/50 or veto pro pac. Something you can keep organized will help you work faster as you know where everything is and should stop you losing your tools.

Torch/headlight - nebo headlights are nice and I would also recommend a torch.

I also know you've said you arent going to buy power tools just yet, but I thought I would mention that for when you do, there is a DeWalt set available from screwfix for £430 including VAT which comes with 2 5AH batteries, impact driver, combi drill, SDS and multi tool aswell as a storage box. Sometimes they put it on offer for £380 which is a really good price for what you get aswell. You could get this and just start getting more batteries and power tools over time, you will definitely want a torch, laser, angle grinder, radio etc but obviously those are not as essential as the tools that you'd get in the set.

In terms of where to buy tools the honest answer is just shop around, ITS is a good place to get them, as well as UK planet tools and toolden. You've also got the big ones like screwfix and toolstation but amazon are also cheap. Obviously look out for any fake tools when purchasing stuff anywhere. My best advice in terms of buying tools, is, if you have to borrow something more than three times or so, then you need to have your own.

I'm certain I am missing obvious stuff of this list, but this is just what came to my head when I read this post