British Prime Minister Margaret Thatcher said yesterday that while she expects progress to be slow and difficult, she has "a real hope" that the U.S.-Soviet arms control negotiations beginning next month in Geneva will lead to substantial reductions in the nuclear arsenals of the two superpowers.

At a news conference ending a three-day visit here, Thatcher also reiterated that Britain agrees fully with the United States in its decision to withdraw from nearly all military cooperation with New Zealand because of that country's refusal to permit port calls by U.S. nuclear warships.

"I am as disappointed as you are over the approach taken by the prime minister [David Lange] of New Zealand," she said. "He knows my view."

British officials have made clear that when Lange arrives in London for a conference later this week, he will be advised that Britain intends to follow the U.S. lead and refuse to have British vessels call at New Zealand ports if they are required to say whether they carry nuclear weapons.

Although Thatcher is known to be concerned about the effects of the U.S. budget deficit on the British economy, she said she had not advised Reagan about how to reduce the deficit or bring down the skyrocketing value of the U.S. dollar.

"I don't think he needs any messages to get the deficit down . . . ," she said. "It's an enormously difficult job, whether in the United States or Britain, and I don't have any list of rapidly ready answers that I could pull out and give to you."