Nigello: No 'Brit' would 'roll their eyes at illicit boozing' anywhere, particularly at two young women having a great time and drinking champagne on a day out! On the whole we don't give a toss what other people do unless it directly affects us in a negative way, which this in no way would. Live and let live.

Some people will tut and roll their eyes at anything. Most would only get annoyed at people who are so kail-eyed as to shouting and 'making an exhibition of themselves', which I'm sure the OP wouldn't. But maybe it's not worth the hassle. If the weather's nice, try the middle of the Millennium Bridge or Hungerford Bridge.

There is a "Champagne Cruise" available for the London Eye. You first ride the eye, without champagne and immediately following ,board a boat for a lovely ride on the Thames (45 minutes). They serve you a glass of champagne on board. You also get preferred boarding on the Eye, so you do not have to wait in line. This is not an economical way of doing it, but quite nice.

To Ralstonian...Where do you purchase that river cruise and Eye combo package? Is the Eye a walkup ticket booth situation..or reservation/purchase in advance only? Thanks.

to Azwurth-
www.londoneye.com , click on book online, scroll down to either champagne cruise (includes Thames River ride) or champagne flight. All other information you need is on this sight. You can purchase tickets there, but there could be a long wait.