You could get a laptop with a touch screen and stylus (i.e. ASUS Vivobook - £500), or you could get a regular tablet with a stylus (i.e. Samsung Note - £360). If it's just going to be for doodling or very simple pictures then those will be fine - and you get the added bonus of then having a laptop or tablet that can do other functions too.
The other option is to get a drawing tablet, which you will need a computer or laptop to plug it into. Think of it as an input device, just like a mouse or keyboard, but with a pen instead.
It will be a struggle to do any significant digital art on a bottom end PC/Laptop, but for amateur artists it doesn't need to be a top-of-the-range gaming rig either! A mid-level machine will be perfectly adequate.
Drawing tablets come in two main flavours: with screen and without screen. The former are more expensive, but are easier to use as you don't have a disconnect between your hand and your eye.
The ones without a screen mean you draw without looking at your hand - which takes a while to get used to. However, that's how most people start out because the cost difference is massive.
You can pick up a small Wacom Intuos (no screen) for around £100. A small Wacom One (screen) on the other hand is closer to £350. Wacom is the big player in the drawing tablet world.
One thing to be wary of is that the pen will likely have replaceable nibs, as these are basically just a thin strip of plastic that wear down with use, due to the friction. If you go for a non-mainstream brand, then getting replacement parts could be a nightmare.
If you decide to go down the path of getting a drawing tablet with a screen, and especially if you go for a cheaper variant, consider whether you might want to get a screen protector. If it's needed, then be ready to replace the screen protector frequently as it'll get scratched with use. Again, these can be hard to source with non-mainstream brands.
You will also need some art software to really get the most of out a drawing tablet. Sometimes tablets come with a trial of some software.
There is free software out there (GIMP, etc) but you get what you pay for... At the opposite end of the scale, Photoshop is the professional level and eye wateringly expensive. I'd suggest looking at something like Clip Studio Paint (£40 - one off payment) as a good half-way house, which you can trial first.