Gonzo has hit the nail on the head there, the other thing to add is if you were in the same vortex category, and flying VFR, then there is no required time separation, however I would question two things, firstly the controllers situational awareness, in the UK, unless specific criteria are met then a landing clearance cannot be issued until an aircraft has vacated the runway, or got airborne (land after or land after the departing), the latter only when specific permission has been granted by the authority and certain criteria will be met.
Secondly, I would question your airmanship skills, are pilots now not taught to check the final approach before entering an active runway, i for one would question a clearance to line up if I saw an aircraft on short final.
My final point is this, you have the right to say, I'll wait for 1 / 2 / 3 minutes for vortex, the controller concerned will no doubt scream and shout, calling you every name under the sun, but it is your right, you are responsible for the safety of your aircraft.
I would suggest you call the tower and try to speak to the controller to discuss the matter