Leaky flat roof

I live in a rented ground floor studio flat which is part of a new annexe recently built next to my landlords house. On the first floor of the annexe is a bedroom belonging to my landlord that which is above two thirds of my ceiling. The other third which sits above my kitchen is a balcony which of course means that this part of my studio flat has a flat roof. All of this, off course, is part of the new annexe, as well Although, there is no problem if the weather is dry or there is moderate rain, during heavy or persistent rain I get water slowly seeping through my ceiling from above where the balcony area is. The water seeps through a cornice but has never reached the floor of my flat (a very slow trickle and only appears with heavy or constant rain). There is also a stain in the ceiling in the centre of the kitchen, although no water has actually dripped through. To solve the problem, my landlord got his regular builders (two or three men who he knows, who are jacks of all trades and who apparently built the new annexe), to completely strip the flat roof/ floor of the balcony and renew the lot. However, the problem persists during heavy or persistent rain. To solve the problem, the landlord wants to send his men into my flat to hack out the ceiling in and around the areas where there is water penetration to find out the exact source of the leaks. I, for obvious reasons, would prefer that he continues to look for the source of the problem on the flat roof/ balcony floor, and that he preferably gets a qualified roof expert to do this check. Which method do you recommend? I know it's hard to fathom without actually seeing the job, but I would gerately appreciate it if you could give a professional and unbiased answer. Thank you for your patience in reading this long question. Yours sincerely, Gary