Thompson's advisers aim to use the London events to bolster his foreign policy credentials and elevate him above the increasingly contentious fray of the GOP race.
On Wednesday, he will pose for photos with Thatcher, which his advisers hope will enhance his support among devotees of former President Ronald Reagan.
Thompson will deliver the foreign policy speech, "Strengthening the Transatlantic Alliance," on Tuesday at the Policy Exchange, a conservative think tank based in London.
It will stress the importance of American alliances abroad, his advisers said.
"The speech is mostly about the unique and special relationship between the U.S. and the U.K," an adviser said on condition of anonymity, because the prospective campaign has not publicly announced details of the address. "It is about how we have a responsibility to stand together and lead the Western democracies, protect our civilization and stand together for freedom."
The audience will include British business, opinion and political leaders.
Thompson will follow it with a dinner Tuesday night with British journalists, businessmen and policymakers.
The "Law & Order" actor and former senator from Tennessee will meet Wednesday with Lady Margaret Thatcher, the United Kingdom's first female prime minister, and David Cameron, the current leader of the Conservative Party.
The foreign trip comes as Thompson prepares for the formal launch of his quest for the Republican nomination, likely in the first few weeks of July.
Thompson also plans a trip to Israel later this year, advisers said.
Even before Thompson's formal entry into the race, his campaign is likely to announce twin headquarters in Northern Virginia, where policy, communications and research will be based; and Nashville, which will be the home of organization, outreach and other departments.
The campaign will also begin rolling out a slate of advisers.
Liz Cheney, the former State Department official and the vice president's elder daughter, is consulting on foreign policy. Longtime GOP guru Mary Matalin, a friend of Thompson, will help shape the campaign's message.
Although Thompson is formally just testing the waters, his operation is quickly picking up the trappings of a full-fledged campaign. He traveled to London with his new personal aide, a former staffer in his Senate office who had gone on to the Republican National Committee.
Advisers were debating an announcement date on Monday, and said it was likely to be in early to mid-July, perhaps a few days later than originally planned.
"That's the starting gun for everyone to start harassing him about why he doesn't know everything about every issue," said one adviser.
Over the weekend, a Mason-Dixon poll published by The State newspaper of Columbia, S.C., showed Thompson leading the Republican field in that crucial early-voting state, with 25 percent, compared with Rudy Giuliani at 21 percent, Mitt Romney at 11 percent and John McCain at 7 percent.
Thompson is scheduled to visit South Carolina for a state party fundraiser next week.