If the conditions are right then particles from fireworks will enhance the potential for fog to form....here's an explanation as to how...
Last night, all the fireworks produced small particles which remained in the air near over the UK overnight. There was smoke last night, but this isn't really fog in itself, more a collection of (larger) soot particles. But as warm(er), moist, sea air moved in from the west, it cooled over the land and as air cools it can no longer hold as much water vapour, so liquid water condensed onto all available surfaces, of which particles were in abundance, hence forming cloud at low level (fog).
A higher temperature inside the tunnel is the most probable reason for the tunnel question - warmer temp enables the air inside the tunnel to retain more water vapour, and so the water evaporates from the surface of the particles leaving the visibility clear. As the air leaves the tunnel at the end, it cools again and produces more fog.
So you still need the main ingredients of fog - moist air reaching cooler land, particles and low wind speed. Particles from fireworks will contribute but to exactly what extent would require some measurements and maths. In my opinion it is likely that you would have had some fog anyway butit has been made thicker and longer lasting by the extra particles.
In the north it has been windy all night, and so the particles have all been blown away...so it is very clear and crisp.