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Yes, you can use the Access UK online visa application service, but you will still need to visit the Visa Application Centre in Rome.
The UK Visa and Immigration guidance on this is quite clear:
1. Applications for short-term visas and EEA family permits
You can make applications for a visit visa, a short-term study visa or EEA family permit in any visa application centre, British diplomatic mission or consular post overseas where entry clearance applications are accepted.
You should be present legally in the country or territory youβre applying from.