Hundreds gathered outside the gates of Westminster Cathedral Hall to pay their last respects. Thousands more are expected to visit the hall, where the cardinal will lie in state until Thursday.
The closed coffin is shrouded with an ivory-coloured cloth sheet with the cardinal's red biretta sitting on top.
His funeral mass will be held at the cathedral on Friday at 11am.
The 76-year-old cardinal, died two months after announcing he was suffering from inoperable cancer.
Mourners will be able to come to the hall between 9am and 7.30pm until Wednesday and then between 9am and 1pm on Thursday, before the cardinal's body is received into the cathedral.