People in Cambridge are far more likely than on average in English cities to ride bicycles because it's made easier and cheaper than the alternatives, not because they're institutional cyclists.
It is rather strange that a discussion about road and rail spending has been dominated by cycling!
I grew up in Cambridge half a century ago, have visited it frequently all my life, and moved back recently. I'm not quite sure what "institutional cycling" means, but cycling in Cambridge isn't easy or cheap, so they can't be the reasons why we do it.
Cycling was a very common form of transport before mass car ownership. Look at archive film footage of workers going home from factories at end of shift. When I was young many people cycled to get to and from school or work. Leisure journeys of fairly long distances would also be done cycling: before they had children my parents would cycle from Cambridge to Bury St Edmunds and Stowmarket to visit relatives.
To digress slightly, only the Fenland part of East Anglia is flat, the rest is just not high. And cycling in the Fens can feel quite hilly in a strong wind.
What's different and interesting about Cambridge is that cycling never fell away in the way that it did in most other parts of the UK once mass car ownership became affordable.
Cambridge has a higher than average student population and the Cambridge colleges have blocked, obstructed and impeded pretty much any development in central Cambridge for the last 2 centuries.
In some ways it's a pity the Luftwaffe destroyed Coventry and missed Cambridge - life could have been quite interesting had it been the other way around.
These are two of the reasons but there are others.
One is the River Cam, which embraces the old centre on 3 sides, and when I was a child there were only 4 road bridges at Fen Causeway, Silver Street, Magdalen Street and Victoria Avenue. I can remember the Elizabeth Way bridge being built.
However there have always been lots of bridges for cycles at Sheeps Green, Garret Hostel Lane, Jesus Green, Fort St George, Cutter Ferry and Green Dragon. We now also have the Equiano and Chisholm cycle bridges.
I still have an old Cambridge street map from the 1970s with proposed roads joining Brooklands Avenue and Barton Road, and Wadloes Road and Cam Causeway (those interested can look those up on a map). Neither got built. That wasn't University obstruction, it was Cambridge people saving the green spaces on Lammas Land, Sheeps Green and Stourbridge Common.
It has always been a lot easier to cross the river by bike than by car.
Another is that Cambridge has also chosen not to increase road capacity by building dual carriageways in residential areas. Apart from a few miles of dual carriageway around Elizabeth Way, with the Grafton Centre coming along at roughly the same time, Cambridge has never expanded road space to meet additional demand.
Similarly, Cambridge has resisted the temptation to provide lots of car parking in the centre. When I was a child the only multi-storey car park was Park Street, though in the 1970s we did get Lion Yard (now Grand Arcade), Grafton Centre and Queen Anne Terrace. Of these only the Grafton Centre has good road access to get in and out. There were all sorts of mad car parking proposals, including an underground car park at Parkers Piece (in the style of Hyde Park in London), but they didn't happen.
Cambridge has kept as much road traffic as possible out of the City, helped by the northern and western bypasses (now the A14 and M11) and five Park And Ride sites on the edge of the city
As a result car journeys within the city suffer badly from congestion and cycling is the fastest and most reliable way to get around Cambridge. Most Cambridge people know that, if they want to be at place X by time Y, the only guaranteed way of arriving on time is to cycle.