The basic mechanicals of the engine all fit right into place, that is, the cylinder head, block, manifolds, mounting points, etc., are all interchangeable insofar as all the bolt holes line up. However, beyond the turbocharger, there may be differences in the injection pump and injectors, strengthening/reinforcements of key engine components and certainly different ECUs.
You will need to modify the exhaust, plumb an intercooler, and also adapt the N75 solenoid. If using a VNT turbo, you need to figure out a vacuum source to actuate the vanes. All are surmountable problems, but they're not trivial.
The least problematic swap would be to lift the whole SDI motor out of the car and drop in a TDI along with the ECU, etc. I assume you're from the UK; there are many well-qualified shops that can do the swap for you, but expect to spend a good deal of money for parts and labour, more than is probably worth it. That considered, consider looking for a Seat Leon or Skoda Fabia, which are both based on the Polo platform and available with 1.9L 4-cylinder TDIs. Or of you manage to find a wrecked TDI Leon or Fabia, you can scavenge all the parts to swap into your Polo.
Does you car have a 64 or 68HP SDI?