Every EU member is obliged to join the eurozone. The EU members who have not yet done so are still to meet the convergence criteria, with the only exception being Denmark who obtained a special exemption (along with the UK) during the negotiation of the original Maastricht treaty.

On the flipside, although Sweden is technically obliged to join the eurozone eventually, it has avoided doing so by intentionally not fulfilling the convergence criteria (by not joining ERM2). Most political parties in Sweden acknowledge it would be in everyone's best interest to join but a national referendum rejected the euro in 2003. The EU seems content to let them do whatever for the time being, so maybe the UK could chart a similar course if it were to rejoin, hypothetically.