Park rangers are expected to start closing the public gardens around 6.30pm with the area set to fully close by 7pm.
Usually the gardens stay open from dawn until dusk - about 10pm just now - and begin emptying about 9pm.
It is understood that police asked the local authority to consider closing earlier because they are predicting the city centre to be busy on Friday night with football fans.
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Throughout the day, pictures have emerged of Scotland fans arriving in London and enjoying themselves in the build up to the big game which is football’s oldest rivalry.
Euro 96 was the last time the two sides met at a major football tournament and this will be the 115th time they have played each other since 1872.