Firefighters from Brighton, Eastbourne, Hove and West Sussex Fire & Rescue Service attended the scene.
They fought the flames with four jets, according to ESFRS.
It said 10 fire appliances attended at the height of the incident, which will be investigated.
Crews spent the morning damping down hot spots, cutting away and ventilating the property.
In an update at 10:25, ESFRS said Nevill Road was being reopened and its response had been scaled down to two fire engines.
The fire service said operations were finished by 11.30.
