If, as the image suggests, both cars arrived together then B should yield to A (A will approach B from the right, give way to traffic from your right on roundabouts).
However, if A elects to proceed, he/she should keep an eye on B, as B may be impatient or may not be aware of the correct procedure.
NB. No one ever has right of way, the highway code never nominates a right of way, it nominates/suggests who should give way.
Insurers usually treat roundabout incidents as 50/50, unless one party has overwhelming evidence (witnesses or camera evidence).
Because, sorting out who did what on driver statements is just about impossible.