And some obvious cultural differences between UK and US (ie: "budget 2 months to find another job". Which made me scratch my head... my experience lately has been 1-2 weeks, if that. And I'm not in a prime market either...)
My shortest job hunt took about a month, but I was a cheap junior dev then. These days, I'm constantly getting pinged by recruiters, but I know better than to take that as evidence that finding a new job would be easy.
My last job hunt took almost 6 months (ok, I was being a bit selective). Hell, finding someone that didn't balk when I told them my current salary (and I was looking for a job in a fairly low COL area) took at least a month (and I'm too old to care about foosball tables and free lattes).
And now my current job has been eroding pay/benefits and layering on useless processes and other BS. I can feel that itch coming on... better budget a year to be safe.
This has been my experience as well. Once I get the itch, I'll start looking, doing interviews and being pretty selective in where and who I want to work for.
I think if you're not in a good place to begin with, you'll take something sooner and inevitably find yourself somewhere you don't want to be.
If you work in a high-demand sector, if you are experienced, if you're not bothered by the ethics of who you work for or about the conditions, and you are lucky, it might take you less time. Good. You saved yourself some budgeted time and you should be happy about this.
There are plenty of jobs where you won't even get through the door in 1-2 weeks. Many companies have hiring cycles that don't allow that level of flexibility.