Last year, I finished my PhD in history and started a 3-year postdoc at a Russell Group university in the UK. I have a few peer-reviewed articles, but haven't published my thesis as a book yet. When is a good time to start applying for permanent lectureships (tenure-track assistant professorships) in the UK?
There is never a perfect time. There is always something to finish, or something important to do to boost your CV.
You should start applying when you feel ready, or perhaps slightly before that. The job market is extremely competitive -- it might take 2+ years and 100+ applications to get your first offer. Better start early and learn by doing.
The time to start applying is now. You are in a strong position, fresh out of your PhD and with a 3-year runway in which to get a permanent job (or find a very good second postdoc that will set you up for a permanent job). This means that for the moment you can be picky and only apply for jobs which you think would be particularly good to have, or for which you think you would be a particularly strong fit. Apply more and more broadly as you get towards the end of your postdoc, until in the last round at the start of your third year you're applying for more or less all the jobs out there (that you would actually take).
I realise that having a book is very important in history, and you may well not be in a position to actually get a permanent job until you've published one, but it's still important to start applying regardless.
- Partly this is because, as others have said in their answers and comments, that you will learn how to write applications and how the job market works by participating in it, not by simply spectating.
- Another reason is that there is a lot of randomness in the job market. For some jobs, you might be more competitive than you think, just because of some alignment of circumstances that makes your profile a particularly good fit even if you're relatively junior. Moreover, opportunities which pass you by now may not come again. The job market in the humanities is very tough at the moment, and may even get worse in the future.
- It is also because even if searches are notionally closed, word gets around. Even if a search committee rules you out as too junior, they might still view you as a good prospect, and that could be communicated to other people in the field. Similarly, if you are applying to permanent positions now your letter writers will also have you in mind if the question of hiring comes up (e.g. at conferences—people talk!). It's good for you to be in as many people's minds as possible as a good prospect, even down the line. Starting to apply now sends a message for the longer term.
All this being said, there is a cost involved in being on the job market. It takes a lot of time to prepare good application materials, and more time still to tailor them to particular jobs. This is time you're not spending doing research and publishing your work. That's why I recommended a staged strategy above, starting with fewer applications and ramping up to more as you get closer to the end of your position, when your profile will be stronger and your materials more polished (but also when you'll need to have another job more urgently). There is also an emotional cost, so again, building up over time can help keep that manageable.