I'm just starting to organise part-time teaching (budgets are falling again) for October. But there's no really definable cycle. And AHRC/ESRC funded post-docs come up as the projects are funded. Again, real cost cuts are ongoing with RCUK funding.
Some things to think about; no need to answer them here.
Are you in touch with the department where you did your PhD?
Have you made personal contact with other nearby universities, and found out who does the hiring?
Are you subscribed to the email list/s for your subject area? We usually put jobs on those as well as jobs.ac.uk
Are you attending conferences in your field, and making a network of your peers - who are both competition but support?
Are you looking in other countries?
Have you looked at EU possibilities via the Marie Curie actions?
Are you making connections with possible sponsors for BA/Leverhulme Early Career Fellowships, which need to be applied for usually from a different institution from where you did your PhD?
Are you developing material for publication? Do you have a sensible publication/research plan for the next 5 years?
A lot of it is about cultivating networks - not in a conniving or venal 1980s style way, but genuine connections with people & groups whose work runs alongside, complements, or connects with yours.
I think nowadays it can be at least 2 years of waiting in the wilderness before really substantial paying work comes along.