As others have said, it varies hugely. A few factors that I’ve seen affect it:
Ministerial interest. Is the policy a priority project that Ministers at Secretary of State level are batting for, is it a side interest for a Junior Minister, or is it an idea that only has the attention of officials? The difference can be staggering, largely to the agenda setting stage yes, but also to how long and with what resources you might formulate the policy, your chances of getting legislation, resources for implementation, etc.
Spending review cycle. Unless you have underspend in your area of significant ministerial interest, if you’re kicking off the policy cycle a long ways out from an SR, you might have a long gap between policy formulation and legitimation.
Day to day official life. How stable is the team leading on the policy cycle? If there’s high turn over, but the policy isn’t a high enough priority to handover in the interim, each person leaving can pause the cycle by ~6 months until the new lead starts.