I love these "how long is a piece of string" conversations!
I have been in consultancy for nearly 10 years and never met anyone who has voluntarily left 1 job to look for another.
Lilly - what are your circumstances in terms of where you want to work, where you are now, etc?
I am based in London but was on a long-term contract in Sheffield. When I decided to change firms, I arranged to spend 1 day per fortnight at the London office to meet a couple of colleagues for lunch etc. I then let my rec agent know my dates and asked for interviews to be slotted in at those times. No-one in Sheffield cared that I was spending time talking about my assignment with experienced colleagues and no-one in London knew what I was doing at the times I wasn't having lunch with them.
Of course this took a while and meant rearranging dates quite frequently but the client always knew their bases were covered.
I can imagine this would be much more difficult if you have no control over your own diary and / or you are "supervised" or micro managed.
I only take leave if the whole process takes more than a couple of hours.