I think one of the key criteria is being close-ish to the Hilton; moving all those people across London in the chill of October before dinner could be a nightmare. So my usual suggestions of Vinopolis and Tower Bridge are out.
The Wellington Arch at the centre of Hyde Park Corner would have been perfect given its location close to the Hilton and quirkiness (plus a nice view of Buckingham Palace Gardens from the roof):
http://www.english-heritage.org.uk/b...llington-arch/
Sadly, as you've no doubt found, it takes only 36 for Dinner and 80 for drinks.
As an alternative, I' recommend the Royal Thames Yacht Club (the building to the East of the Mandarin Oriental):
www.royalthames.com/Functions.aspx
Walkable, decent view of Hyde Park and not somewhere most will normally visit.
As an alternative Peyton & Byrne should be able to satisfy your requirements at one of their government/gallery venues:
www.peytonandbyrne.co.uk/venues/index.html
I've been to Lancaster House and it was excellent;
I've been to an event at the Royal Academy they did, and Burlington Gardens is also worth a look.
Would be terrific to get the Durbar Court, heart of the Foreign & Commonwealth office, but I'm unsure whether you'd be swamped in that space:
FCO Fine Rooms are similarly impressive and more intimate:
If you're feeling brave, you could try the Playboy Club which has the advantage of being almost next door to the Hilton; I understand the fish is excellent, the beef less so
http://playboyclublondon.com/private-hire/
Finally, in the centre of Hyde Park, there is the new-ish Zaha Hadid-designed extension to The Magazine - a pleasant walk through the Park from the Hilton, and you could no doubt have drinks beforehand in the adjacent art gallery:
www.serpentinegalleries.org/restaurant