2001 Holden Astra Ongoing noise problem

Hi there, I've just brought an 01 Holden Astra thats done 130000kms from a car dealer in Brisbane. After a long list of problems have been fixed including engine mounts, all new brakes, timing belt, major service etc. There is still an annoying whirring noise (which was the initial complaint) that occurs here and there but certainly everyday, it starts quietly then gets quite loud and sounds like it's coming from the rear of the car but I can't be sure. It sounds like a woowoowoo sound and stops immediately when I touch the brakes and restarts as soon as I take my foot off them. I thought it was a wheel bearing but am not sure, the mechanic up in Brissie said he thinks it could be a tyre which is definitely isn't (tyre specialist confirmed it wasn't here on the coast). It happens when I am driving any speed not when I turn it even happens when I reverse in the morning. The sound is like the steering when there is not enough power steering fluid but is definitely not. I would really appreciate your opinion and can provide more information, please contact me on courtney_upton19@hotmail. Com