Forget 200£.

200£ per axis is closer to the truth, if you want anything with decent accuracy, repeatability, and resolution.
And that is in materials costs, alone.

Anyone can make decent high-precision mechanicals, per axis, with any decent lathe.
But it is cheaper and easier to buy them, and they cost more than 100£/axis, and a lot more for really good ones.

Define your expected usage, payload, repeatability, speed, and resolution.