I assume you have a poor neutral connection external to your property. Also you quite likely have a N - E fault internal to your property, do an insulation resistence test, if clear approach your supplier and ask him to rectify the external problem.
Neutral is obtained from the centre point on the transformer, centre point is also grounded to earth via a rod at source. Your reading at the property to earth I would expect to be in excess of 100 ohms, hence the differing potentials. Have you carried out a insulation resistence test on your...
A TT system relies on an RCD and an adequate return path to the transformer. A 60v reading between N & PE is not exceptional ,as they are at different potencials. I would advise you to loop test your PE and carry out an RCD test at the rated mA. Tripping during high winds is a problem in Spain...