set of electrician's screwdrivers, a socket tester, cards of different cartridge fuses (3A, 5A, 13A) and a basic multimeter.
Don't get a neon screwdriver, they give misleading and unsafe results
I say a set of electrician's screwdrivers, although you will probably only use two sizes most of the time, because you can buy quite reasonable quality ones, in sets, in the DIY sheds for £10 or so. They have brightly coloured red and yellow insulated handles, and the blade is insulated as well. They are called VDE tools and are tested for safety. They are usually made of Chrome Vanadium steel, which is strong and hard. You can use them for other screws as well so you will end up with a handy household set. Cheap screwdrivers wear out quickly and will annoy you. Buying a set of 4 will probably be cheaper than buying two individually
This set in
wickes is £8.80 and reasonable quality. You might find a set with matching pliers. Only buy it if both pliers and screwdrivers are Chrome Vanadium steel. If not, it is cheap rubbish. "Carbon Steel" is not good enough.
You can get a basic digital multimeter for £10 or so. The cheap ones have poor quality test leads
so if you have a choice get one with thicker-looking leads. you can use this for continuity testing and other things like testing a kettle element or a lamp to see why it will not switch on (e.g. if the switch or flex is damaged) but we will tell you more about that when you need to know.
A socket tester does some basic testing of the circuit, it only detects quite gross errors, but it will at least tell you when to get an electrician in.
I think you can get a cheap one for £10 or less. mine is a Martindale, Fluke do a very good one which will be a lot more.
Have a look in your fusebox" (consumer unit) and describe what you see (there are at least three possibilities) or post a photo if you can. It may have a pull-down flap that you can safely open.
A metre or so of green-and-yellow-sleeving that you will need if you ever need to look at or change a socket or a light fitting
A roll of White Vinyl Tape and a permanent marker pen (you will need this (probably) to identify the circuits in your consumer unit (by using it to make label strip) and if you ever take a light fitting off, it is absolutely vital to identify and mark every wire before you disconnect them
A strip of plastic "choc block" connector (you will often need this and it is very cheap.
you will probably mostly use the 5Amp size but you might occasionally need 30A so if you can buy them singly for less than a pound, get one of each. It will probably last you years. If you only get one size, get 30Amp
A wire stripper for talking the insulation off wires (e.g. when changing a flex or fitting a plug) can save you damaging your teeth or blunting the carving knife or cutting your fingers off.
There might be a set containing a useful starter kit in the DIY shed or hardware store, but they are often very poor quality.
I still recommend that you read one of the books I mentioned. It will tell you lots of useful things, including those you didn't know you needed to know. And there is some useful stuff on
//www.diynot.com/pages/el/