Fabulous mid-century modern building designed by the fabulous Finn Eero Saarinen! I read that it is being remodeled as a Rosewood hotel. I wonder if they will keep the eagle.
I think it's walking distance - about 30 minutes to Soho - how about The Dog and Duck?
https://www.nicholsonspubs.co.uk/restaurants/london/thedogandducksoholondon#/
Or slightly farther, The Rules.
https://rules.co.uk/
You get a nice view of Rome from the Cavalieri.
It's currently a Waldorf Astoria, but when I stayed there in 2004, it was a Hilton, and had the best club room ever. This was the view on a hot smoggy, summer day.
And then later I found this photo my uncle had taken from there in 1965.