As tuffty said i too have a bad fuel pump, so bad that as soon the turbo starts to spool up fuel pressure goes down to 2 bar (with 3 bar fpr)
Fuel pump swap is pretty much straightforward, if you want to save some quid you could buy only the swirl port and pump and use your lid, fuel sender, ring screw and rubber seal.
AUDI A3 TT 1.8T 3.2 V6 INTANK FUEL PUMP 183VG0630 | eBay
Or this complete
OEM AUDI TT QUATTRO (8N) - Fuel Pump 02-06 | eBay
Before you buy make sure you tell them your chassis number, there are 2 types, pre 2002 and post 2002.