Commuter services were certainly affected. A general slowing down of traffic, poor visibility and the associated accidents when people fail to take conditions into account invariably have an effect on timekeeping.
As an example, the M2/A2/A102 got no higher than 40 mph for most of the way between Gravesend and the Blackwall Tunnel for the last two days, and had significant sections quite a lot slower (i.e. 4 mph) than that.