Hi
No, they're not obliged to provide but they are obliged to look and see if they can provide, given constraints such as land, finance, whether spare land,funds would be put to better use etc. Not sure of the numbers e.g. whether it's 6 or more than that. NSALG should be able to advise (
www.nsalg.org.uk)
Have you tried neighbouring councils? I didn't want to take any of the sites in my Borough council (Reading) so have taken plots in Wokingham District area. Some councils/parishes allow this.
Also..don't necesarily believe that no plots are available. This usually means all plots have rent paid for the year, but some will no doubt have not been cultivated and it's usually within the contract that if the allotment is not cultivated then the council can end the contract with that tenant. Get a list of sites, go and visit them and have a look - if you see someone, call them over and ask if any of the plots aren't being cultivated.