Hi Adrian, as Steve said you have to get the engine code which will definitely be in the handbook, armed with that just google Audi A4 2011 [engine code] oil consumption problems, that will throw it up, can you please confirm petrol/diesel as both engines are very different problem wise, if its a 2.0 petrol it is probably suffering the ring problems, as for getting it rebuilt I would asses that would be the thick end of £4000 and you may be better served buying a reconditioned unit from eBay and just bolting on your ancillaries from the old engine, other than that you can try to live with it.
Steve.