Models for the lens and source of B0218+357 - A LensClean approach to determine H0
B0218+357 is one of the most promising systems to determine the Hubble constant from gravitational lenses. Consisting of two bright resolved images plus an Einstein ring, it provides better constraints for the mass model than other systems. The main problem left until now was the poorly determined position of the lensing galaxy. After presenting results from classical lens modelling, we apply our improved version of LensClean which utilizes the Einstein ring for lens modelling purposes. The primary result using isothermal models is a well defined lens position which allows the first reliable measurement of the Hubble constant from this system. The result of H0=(78+-6) km/s/Mpc (2 sigma) is high compared with other lenses but compatible with the HST key project and WMAP results. We furthermore discuss effects of different radial mass profiles. The power-law exponent of the potential is constrained by VLBI data to be beta=1.04+-0.02, very close to isothermal. The effect on H0 is expected to be very small. We also present a composite map (lensed and unlensed) which shows the rich structure of B0218+357 on scales from milli-arcseconds to arcseconds. Finally we use a comparison of observations at different frequencies to investigate the question of possible weakening of one of the images by propagation effects and/or source shifts with frequency. The data clearly favour the model of significant extinction without noticeable source position shifts. The technical details of our variant of the LensClean method are presented in the accompanying Paper I.