why queen is more preferred over king in Britain ?

Its not like that. The succession was incidental. The father of current queen didnot have any sons. She was the only eligible successor. Even now if the eldest child of the monarch is a daughter then britain will have a queen and if the eldest child is a son then a king. Its not about preferring a king or a queen. The first eligible successor will be crowned whether its a king or a queen. As for the present scenario the successors of the current queen are sons, so britain will have a king as their next. Had the oldest successor been a daughter britain would have had another queen.