Do i need a visa or does the 144 days pass cover us

Going to shanghai staying 2 nights in a hotel pre cruise,leave Shanghai on ship,going to 2 ports in South Korea,then in to Bejing for 3 nights on-board the ship,do we qualify for the 144 days.or do we have to buy the visas.
Travel agent has given me the wrong info,just found out about this.We are British with UK passports.How much will they cost.