Patients will be randomised to receive either: lapatinib 1500 mg daily, trastuzumab 4 mg/kg intravenous (IV) load followed by 2 mg/kg IV weekly, or lapatinib 1000 mg daily with trastuzumab 4 mg/kg IV load followed by 2 mg/kg IV weekly for a total of 6 weeks. After this biological window, patients on monotherapy arms will continue on the same targeted therapy plus weekly paclitaxel 80 mg/m^2 for a further 12 weeks, up to definitive surgery. In the combination arm, patients will receive lapatinib 750 mg daily in combination with trastuzumab 2 mg/kg IV plus weekly paclitaxel 80mg/m^2 IV for a further 12 weeks, up to definitive surgery. After surgery, patients will receive three courses of adjuvant chemotherapy with 5-Fluorouracil Epirubicin Cyclophosphamide (FEC) followed by the same targeted therapy as in the biological window of the neoadjuvant setting for a further 34 weeks (in the combination arm, lapatinib dose will be 1000 mg daily in combination with trastuzumab). The planned total duration of the anti-HER2 therapy will be one year.