From what I can tell, Bond seems to be slightly east of Westminster, looking west; following the line of the Thames, that would seem to put him close to the old Ministry of Defence building (appropriately enough)... can't quite give you an exact spot, but looking at the 'bell tower' on the right of the picture, it seems possible that he's on the roof of the Guoman Royal Horseguards Hotel, though I'm not quite sure...
If it is the hotel, you might be able to get to that spot, though if it's a government building you may be less lucky! If you want to get close to the Vauxhall Building as featured in TWINE, you may want to take a 'Duck Tour' - these are tours of London in DUKWs, the amphibious vehicles which were used in the D-Day landings, and after driving round the centre of London for a while they go into the Thames and travel east (the same direction Bond travelled in as he chased the Cigar Girl, though the Ducks don't go as far east as the Dome). The nice thing is that the ramp they use to get into and out of the Thames is right next door to MI6. "Take photos by all means," the guide said when I last did the tour, "because you can be sure they're filming you!"
The Oxo Tower has a good view out onto the Thames, and you don't need to dine there to go out ont the balcony (just buying a drink will suffice).
If you're feeling adventurous, you can climb up the side of the Millennium Dome (now known as the O2, it's become a popular entertainment venue) and admire the 360-degree views - details here. Just be careful you don't tumble down the side of the building as Bond did in TWINE!