For the first time the possible presence of radial gradients of magnetic fields in the atmospheres of three magnetic Ap stars has been critically examined by measurements of the mean magnetic field modulus from spectral lines resolved into magnetically split components lying on the different sides of the Balmer jump. A number of useful diagnostic lines below and above the Balmer discontinuity, only slightly affected by blends, with simple doublet and triplet Zeeman pattern have been identified from the comparison between synthetic spectra computed with the SYNTHMAG code and the high resolution and $S/N$ spectra obtained in unpolarized light with the ESO-VLT UVES spectrograph. For all three stars of our sample, HD 965, HD 116114 and 33 Lib (HD 137949), an increase of the magnetic field strength of the order of a few hundred Gauss has been detected bluewards of the Balmer discontinuity. These results should be taken into account in future modelling of the geometric structure of Ap star magnetic fields and the determination of the chemical abundances in Ap stars with strong magnetic fields.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html