B0218+357 is one of the most promising systems to determine the Hubble constant from time-delays in gravitational lenses .
Consisting of two bright images , which are well resolved in VLBI observations , plus one of the most richly structured Einstein rings , it potentially provides better constraints for the mass model than most other systems .
The main problem left until now was the very poorly determined position of the lensing galaxy .

After presenting detailed results from classical lens modelling , we apply our improved version of the LensClean algorithm which for the first time utilizes the beautiful Einstein ring for lens modelling purposes .
The primary result using isothermal lens models is a now very well defined lens position of ( 255 \pm 6 , 119 \pm 4 ) mas relative to the A image , which allows the first reliable measurement of the Hubble constant from the time-delay of this system .
The result of H _ { 0 } = ( 78 \pm 6 ) \text { km } \text { s } ^ { -1 } \text { Mpc } ^ { -1 } ( 2 \sigma ) 
is very high compared with other lenses .
It is , however , compatible with local estimates from the HST key project and with WMAP results , but less prone to systematic errors .
We furthermore discuss possible changes of these results for different radial mass profiles and find that the final values can not be very different from the isothermal expectations .
The power-law exponent of the potential is constrained by VLBI data of the compact images and the inner jet to be \beta = 1.04 \pm 0.02 , which confirms that the mass distribution is approximately isothermal ( corresponding to \beta = 1 ) , but slightly shallower .
The effect on H _ { 0 } is reduced from the expected 4 per cent decrease by an estimate shift of the best galaxy position of ca .
4 mas to at most 2 per cent .

Maps of the unlensed source plane produced from the best LensClean brightness model show a typical jet structure and allow us to identify the parts which are distorted by the lens to produce the radio ring .
We also present a composite map which for the first time shows the rich structure of B0218+357 on scales ranging from milli-arcseconds to arcseconds , both in the image plane and in the reconstructed source plane .
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 .