A Royal Navy spokeswoman confirmed there had been an increase in local security personnel at the base.
But she stressed that the increase was at the commanding officer’s discretion, and not as a result of any direct threat to the base or local area.
The threat level for the area outside the M25 remains at ‘severe’.
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Seven people have been arrested in connection with yesterday’s incident, in which four people - including the attacker - died.
The victims include unarmed police officer PC Keith Palmer, 48, who was stabbed by a man armed with two large knives inside the grounds of the Houses of Parliament.
Hampshire Constabulary has said there is no specific intelligence to suggest an immediate threat within the county.
Chief Constable Olivia Pinkey said: ‘Our thoughts are with the families, friends and colleagues of those killed and seriously injured as a result of the events in London yesterday.
‘As is standard procedure whenever an incident like this happens, whether in the UK or abroad, we are reviewing our security procedures and resources to ensure that they are appropriate and if any changes need to be made.
‘We have also reviewed all pre-planned events taking place in Hampshire and the Isle of Wight in the coming days, as is normal procedure, to ensure all plans are up-to-date.
‘At this time we are satisfied our plans are robust but we will continue to review the situation and follow any national guidance.
‘We understand that the events in London yesterday may cause people to worry but we would renew our advice to our communities to be alert but not to be alarmed.
‘We would advise members of the public to remain vigilant and if you see anything that causes you concern or raises your suspicions do not hesitate to call the Anti-Terrorist Hotline on 0800 789 321, or 999 in an emergency.’