Can be many variables - but...
2020-21 Anecdotal on a straightforward 3.6m back extension in outer NW London -
Initial client contact September 12th
Planning submitted December 24th
Planning approved Feb 16th
Engineer site visit March 11th
Structural drawings received April 27th
Tendered to contractors May 7th. but start dates not sooner than October and many looking to book for 2022 as a preference - also prices likely to be +30% up
so basically 3.5 months up to planning, 2 months standard planning consultation period, 3 months to being ready to tender to contractors. You can run the detailed design/engineer's work whilst it's in for planning but there is risk of abortive work should the design need adjusting or not get permission at all.