The ice level in London is not consistent. The ice is near the top of the buildings at Canary wharf but Westminster palace is not under the ice and it is around the same sea level.
The British soldiers seen appear to be using the US M16 rifle. British soldiers would be issued with L85 rifles (commonly known as the SA80).
Considering the extreme cold conditions as portrayed in the movie, there is never any sign of air vapor coming out of the mouths of the actors. Which can be seen in the air as a cloud, similar to fog.