At a meeting in the Zhongnanhai leadership compound, Lady Thatcher posed with Mr Li, saying that it was "very nice to be here". But when they took their seats in the ornate reception room, the former prime minister went straight to the point, even before spectators could be ushered out.
Lady Thatcher said: "Thank you very much for giving me time to talk together. I think we should talk about the remaining problems in Hong Kong, with but a short time available to solve them, and also about the many exciting things that are happening in China now."
Mr Li said: "I'm ready to talk with Lady Thatcher about all the issues you are interested in," to which Lady Thatcher replied: "Thank you. That would take a very long time." (Laughter.)
Lady Thatcher went on to say there were "quite a number of things to be solved and two years isn't very long in which to solve them... But it is long enough, as long as we get on with it."
Looking impatient, Lady Thatcher then suggested to her hosts that it might be time for the audience to leave. As everyone left, her voice could be heard saying: "I never forget that I signed the Joint Declaration."
The 1984 Sino-British Joint Declaration was the agreement under which Hong Kong will revert to Chinese sovereignty in 1997. It is 20 months since a cabinet minister has been welcomed in Peking, so there is some interest in Lady Thatcher's agenda. She is said not to be acting as an emissary for the British government, nor to be here to negotiate. But her visit is seen as a sign that Sino-British relations are stabilising.
But it seems unlikely her meetings will solve outstanding problems over the transfer of sovereignty and her arrival yesterday was overshadowed by that of King Juan Carlos and Queen Sofia of Spain.