Outdoor Afternoon tea in London

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Any recommendations for outdoor afternoon teas in london for a group of 6 women with 3 vegetarians?
Would be a friday afternoon.

Ideally a rooftop would be lovely but am struggling to find anywhere with good food and that has seating situated outside.

Please help!

Number Sixteen in South Kensington
Corinthia Hotel
Gallery Mess at the Saatchi Gallery
The Goring

Number Sixteen looks great, thank you!

Both Corinthia and Goring look to be indoors.
Saatchi seems to be in the pedestrianised area so not really what i was looking for.

Thank you!