One of the problems with persuading a local authority to install a crossing is that the mathematical models that are used in assessing the need for a crossing often require that lots of people must already be crossing at or near the relevant point. If only a few people want to cross there the criteria won't be met but equally, if thousands of people would like to cross there (but simply can't because it's presently far too dangerous) then the number of people using any potential crossing will falsely appear to be low to merit the installation of one.
The basic test that many local authorities apply is the PV² one. They count the number of vehicles using the road over an hour and square that number. They then multiply that figure by the number of pedestrians crossing a 100m stretch of the road at that location, to arrive at a 'PV²' figure. (In practice they actually do that across the day and then take the average of the four busiest hours). If the PV² figure is less than 20 million, then it is assumed that no crossing is required. If the PV² figure is above 20 million, then further investigation is undertaken.
One doesn't have to be Einstein to see where some of the flaws in that model might lie. If, for example, there is a peak half hour period in the morning (where there are loads of kids crossing the road on their way to school, just as there are loads of commuters going to work) and a peak ten minute period in the afternoon (when there all of the kids come out of school simultaneously but commuter road traffic hasn't started to build up for the evening peak), taking the average of the four busiest full-hour periods over the day (when there aren't actually many people crossing the road for most of the time) is unlikely to yield a sufficiently high PV² figure to merit the installation of a crossing.
Some authorities are now moving away from solely using a 'raw' PV² model, and weighting their figures to take account of the types of pedestrians involved (e.g. unaccompanied children, elderly people, pedestrian with pushchairs, etc) and other factors, such as the proximity of any proposed crossing to a school. However, with financial constraints pressing down upon them, council officials can still be tempted to use PV² as a justification for turning down a crossing request.
I suggest that, as well as contacting council officials, you should directly contact the council itself. (i.e. don't just write to the council offices. Find out who the local councillors are for that area and ask them each to support your campaign).