The government (whoever is in charge) make too much money from the motor car to ever seriously consider reducing reliance on them.
As
@Moodyman mentions upthread, we've had the hideously expensive Cycle Super Highway (CSH) put in, and if I wanted to I could virtually cycle from my door into Leeds and then on to Bradford on it. I won't though as huge sections of it are either shared path and too narrow, or frankly crap and should never have been signed off.
Sections where you're forced into the door gap against parked cars, road intersections which are crossed with several toucan crossings, none of which link up so you have to stop at all of them. Bits where it simply doesn't fit so they've painted a narrow cycle lane on the side of a 40 mph dual carriageway to link other bits together. Add in the fact that it's not even the most direct route and you start to see the problem.
Get to the centre of Leeds and it just stops - no signs, nothing. They are now working on putting provision in place, but guess what - more toucan crossings and work proceeds at a glacial place. The city centre section wasn't included in the original back of a fag packet plan, apparently.
If I want to use public transport (and provision, on paper at least, is fairly good around here) then buses and trains don't tie up - First runs the buses, Arriva the local trains and the PTA are unable to get any sort of joined up service or ticketing plan in place. And as
@classic33 has mentioned, the railway seem determined to make taking a bike on the train as difficult as possible.
Using the car to work takes 45 minutes, public transport (on the occasions it works) takes double that.