The Government has not carried out an assessment of, or made projections about the use of, cycle lanes in English cities: this is a matter for local highways authorities.
The Department’s statistics on cycling and walking, published most recently on 18 January 2018, contain information on national cycling trends over time and include some information at a local authority level, but do not cover the use of cycle lanes in individual cities.
Similarly, the Department’s regular road traffic statistics provide estimates of the vehicle miles travelled each year in Great Britain, by vehicle type, including pedal cycles, but do not distinguish between cycling on cycle lanes and cycling on the main carriageway.
The Department for Transport has made funds available to eight cities through the Cycle Ambition programme to improve or expand cycle routes in line with local priorities, and will monitor and evaluate the impact of this funding over time. Other organisations have produced reports which contain some information on this. Sustrans, for example, has recently published “Bike Life” reports for several cities which are available online and which cover matters such as cycle infrastructure provision, travel habits, and attitudes towards cycling in the cities in question.