Florence - 1 and a half hours.
Pisa - 2 and a quarter hours.
Bologna - 2 hours
Forli - 2 hours.
Rimini - 2 hours
Perugia - 1 and a half hours.
Rome - 3 hours
Venice - 4 hours
Take the Eurostar, or any other train, from London via Paris (or from Rome) and onto Florence.
Change at Florence for Arezzo, a journey of around 40 - 90 minutes. You can then catch the bus from outside the railway station to Anghiari.
NB There is a railway station immediately outside Pisa and Rome airports, and therefore it is easy to get to Anghiari by train and bus for those without a car.
There is a ferry from Split to Ancona: it is then a longish and lovely drive across Marche, into Umbria and up to La Ceruglia.
Car Hire is possible through all the international car hire companies at each of the airports mentioned. There is also car hire available in Arezzo and Anghiari.
Taxis and Buses
There are local taxis and buses.