In b4 Take her up the Gherkin? Oxo tower? [insert innuendo] etc..
this might fit the bill - haven't been here myself though do intend to at some point as it's had good reviews
http://the-araki.com/
only seats 9 diners and you get a set menu, very well reviewed, £300 a head , so I guess fits the "exclusive" criteria.
or for a suggestion I have been to a few times
https://sketch.london/
has been there for a while but if you (or more importantly her) haven't been there before then it could be a novelty, can eat there, drink at the bar etc.. very unusual toilets shaped like egg shells