Can you solder?
Actually building a robot is a lot more involved than building the 'Real Robots' one because it was essentially a kit that came piece by piece with a magazine.
£10-15 is a little low for a full robot, BUT, it's enough to build the basic circuitry for the $50 robot (if you can solder).
While you're building that you could be saving for other parts. One of the great things about Admins $50 robot tutorial is that you don't specifically need to use fancy materials if you can't get or afford them. All you really need is a little ingenuity, time and patience.
As for servos and the likes, you can salvage these from r/c stuff too (in cars they are normally used for steering.
The difference between a motor and a hobby servo is that a motor will need a circuit to interface to the microcontroller (the microcontroller can't supply enough power to it) and will more than likely need a gearbox (or really tiny wheels). A servo is a motor with a gearbox and some circuitry to drive the motor already wrapped up in a nice little box. There are other differences but at this point i wouldn't worry too much about it.
If you do choose to follow Admins tutorial I would try to stick to servos as this will make it easier. If you can't get the hitec servos recommended just post a question asking if the ones you have seen are suitable (before buying them).
You'll need to buy a programmer too, if your computer has a serial or parallel port you could save a bit of money on the programmer by buying/making an older version << thats for the avr microcontrollers and possibly one reason avr uControllers became really popular, i have no idea if you can buy or make a cheap programmer for PiCs or any other chip producer.
The problem you're facing now is one that many have faced before: Starting from nothing.
It costs money
It takes time
It requires patience
Best of luck