Regarding your entry to the UK, Gayot already gave a good answer:
No problems resulting from having studied in Italy previously. Itinerary, onward transportation, valid premise are needed just like any other arrival.
Regarding your subsequent visit to the Schengen area, there should also be no issues. As an Australian you may enter the Schengen area for up to 90 days out of 180 and your previous stay on a student visa won't count. The relevant regulation is the Schengen Borders Code and in particular article 5:
- For intended stays on the territory of the Member States of a
duration of no more than 90 days in any 180-day period, which
entails considering the 180-day period preceding each day of stay, the
entry conditions for third-country nationals shall be the following:
1a. For the purposes of implementing paragraph 1, the date of entry
shall be considered as the first day of stay on the territory of the
Member States and the date of exit shall be considered as the last
day of stay on the territory of the Member States. Periods of stay
authorised under a residence permit or a long-stay visa shall not be
taken into account in the calculation of the duration of stay on the
territory of the Member States.