I have, actually, seen the TV movie. I have a mad love for Paul McGann, even if the movie is pure CRACK.
My logic is that it's roughly 8 feet to the top of the sign. Jack's a little over 6 feet tall, and the average distance from a person's nose to their fingertips is a yard. He might have to stand on the little ledge by the base and stretch, but I think he could reach. On top of which, the TARDIS used (http://www.relative-dimensions.net/Police%20Box/images/tardis-new%20with%20doctor%20and%20romana.jpg) to be (http://www.doctorwho-devious.com/doctorwho-devious_images/jonptardis006.jpg) shorter (http://newsimg.bbc.co.uk/media/images/39405000/jpg/_39405202_tardis203.jpg), as far as I can tell, so who knows what the actual dimensions are? (Possibly the dimensions change slightly every time it rematerializes - slight fluctuations in the chameleon circuit? Yeah, coming up with logical reasons for why things happen in Doctor Who is probably a bad idea.)
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My logic is that it's roughly 8 feet to the top of the sign. Jack's a little over 6 feet tall, and the average distance from a person's nose to their fingertips is a yard. He might have to stand on the little ledge by the base and stretch, but I think he could reach. On top of which, the TARDIS used (http://www.relative-dimensions.net/Police%20Box/images/tardis-new%20with%20doctor%20and%20romana.jpg) to be (http://www.doctorwho-devious.com/doctorwho-devious_images/jonptardis006.jpg) shorter (http://newsimg.bbc.co.uk/media/images/39405000/jpg/_39405202_tardis203.jpg), as far as I can tell, so who knows what the actual dimensions are? (Possibly the dimensions change slightly every time it rematerializes - slight fluctuations in the chameleon circuit? Yeah, coming up with logical reasons for why things happen in Doctor Who is probably a bad idea.)