More than 40 firefighters worked to put out the blaze, which started in the early hours of the morning, but many are still at the scene of the incident.
Crews from Gosport, Fareham, Portchester, Southsea and Botley are said to have helped in putting out the fire.
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Speaking on Twitter, Hampshire Fire and Rescue Service said: ‘Thankfully, no-one has been injured. ‘Neighbours in the area may wake up with smoke still in the air.’
The unit, to the left of Solent Funeral Services, is badly damaged.
Residents are being asked to keep windows closed to avoid smoke inhalation.
Firefighters are still working to make the scene safe, but the high street is expected to remain closed for some time.