Monopoli is extremely well connected and easily reachable via air, rail and major roads.
Air (from UK):
British Airways flies direct to Bari from London Gatwick three times a week (Tuesdays, Thursdays, Saturdays) except winter months.
RyanAir flies direct from London Stansted to Bari four times a week (Mondays, Wednesdays, Fridays, Sundays); and to Brindisi from Stansted three times a week (Tuesdays, Thursdays, Saturdays).
Alitalia has many flights to Bari and Brindisi from London Heathow every day, via Rome or Milan.
Monopoli is on the main rail line from the major cities, with Eurostar Italia and Intercity trains stopping in the town, as well as frequent regional services.
Monopoli is easily accessed from the SS16 (aka route E55) which runs the length of the region along the Adriatic coast. The SS16 is the direct continuation of the main A14 Bologna-Bari motorway (also E55).
To the apartment:
The apartment is in the old town, very near the old port, just between the main street Via Orazio Comes and Piazza Palmieri. Although it is possible to drive to the apartment, the easiest way to reach it is on foot, only a few minutes walk after parking at the port.