GWEN IFILL: Joining me now to discuss today's historic events and this remarkable time in the U.K. is Sir Peter Westmacott, a longtime diplomat in the British Foreign Service. He left his post as British ambassador to the U.S. earlier this year, and served before that as ambassador to France and Turkey.

Mr. Ambassador, welcome.

It's been a head-spinning day, a head-spinning time. How are things now doing in Britain? What can you tell us about Britain now?

SIR PETER WESTMACOTT, Former Ambassador, United Kingdom: Well, it's good to be with you again.

I think we're all still a bit shell-shocked, but I think the main change that's happened in the less than three weeks, can you believe it, since the referendum is that even those people who thought it was the wrong outcome and felt that the campaign to leave the European Union was based on a lot of misrepresentation and fraudulent facts and so on, everybody has more or less come to terms with the fact that this is going to happen, the negotiations are going to begin, even if many of us believe that, at some point before the deed is done, the British people will need to be consulted again, either in a general election or in another referendum and so on.

But, meanwhile, the political drama has accelerated with great speed. David Cameron, prime minister, chose to resign, thought that he was going to be there until the 9th of September, and, boom, suddenly, in a couple of days, because there was no other candidate but Theresa May to succeed him, he finds that the removal van has arrived and he's left and he's been to see the queen. And we have a new prime minister and we have half a new Cabinet, well, not quite half, but a number of senior positions already announced.

So I think the mood is one of some surprise, amazement at how quickly things move, and coming to terms with new realities.

GWEN IFILL: Tell us about Theresa May. You know her. Tell us what we can expect of her.

SIR PETER WESTMACOTT: Well, I knew her, saw a good deal of her when she came to stay with us when I was ambassador in France, when we had big migration issues, and also, of course, when she used to come to Washington.

I think she's a very businesslike, no-nonsense person. She's not someone who has cliquey personal entourages. She is very grounded. she comes from a humble, straightforward background, a vicar's daughter. And I'm a vicar's son myself, so I can say these things.

She is very professional. She does her homework. She likes to get her way, I would say. And she makes up her mind and she's pretty hard to shift unless you are very, very sure of your ground. But she has made a couple of speeches in the last day or two which are extraordinarily inclusive and very centrist, even, I would say, and quite surprising for somebody who was considered to be on the right of the Conservative Party, about the importance of the British people coming together and of a government which is for all the people and not just the privileged few.

So, I think that may have surprised a few people, but encouraged a lot of people as well.

GWEN IFILL: She moved quickly today to fill her Cabinet, including making Boris Johnson, who declined to run for prime minister, her — to make her foreign minister, and Philip Hammond her finance minister. These are the two men who are going to have execute these Brexit negotiations.

SIR PETER WESTMACOTT: Well, they are, but they're also going to have one other key player is going to be the leader of the negotiation, of whatever it's going to be called, the department of the withdrawal from the European Union, who is going to be David Davis.

So, Philip Hammond, you're right, my old boss, extremely knowledgeable about accounts, numbers, an experienced negotiator, understands budgets, sorted out the finances of the Ministry of Defense when he was defense secretary, he's gone to Treasury. And I think that is an appointment that will be widely welcomed.

I think the appointment of Boris to the Foreign Office was probably a surprise as much to him as to many other people, because after the referendum, which seemed — the result of which seemed to surprise him, he didn't appear to be quite clear what he did next and made a number of statements which suggested that nothing was going to change between Britain's relationship and the European Union.

So I think he will be thrilled. Obviously, he's visibly delighted to go to the Foreign Office, born in the United States of America, partly Turkish, partly American, great cosmopolitan, extremely cultured man, speaks lots of languages.

He will have a wonderful time in the Foreign Office. And he will not, I suspect,be in the lead of these particular negotiations. I think that will be left to the other ministers largely, but I'm not sure about that. That depends very much on how the prime minister handles it.

And my guess is that her own relationship with Angela Merkel is going to be critical to the success of those negotiations, too.

GWEN IFILL: Does David Cameron leaving the scene so quickly today, does he leave behind a legacy of failure or success?

SIR PETER WESTMACOTT: I think, curate's egg, probably, some good stuff, some bad stuff. I think my own view is that the grand coalition that he was bold enough to create when he didn't win a majority in the general election in 2010 was a remarkable piece of political accomplishment. I think the coalition government between the Lib Dems and the Conservatives worked very well for the first parliamentary term between 2010 and 2015.

In some ways, it smoothed the corners, if you like, of the policies of each party. And demonstrably the prime minister and Deputy Prime Minister Nick Clegg got on very well. And I think they got some good business done, so I think that was a plus.

I think the way in which he got the British economy going after the meltdown of 2008 and 2009 was pretty remarkable. The United Kingdom has a level of unemployment which is less than half the European average. We have been growing at the fastest rate of any European Union country for the last three years. Along the United States, we have been leading the Western democracies out of recession.

They have cut the deficit by more than half. So I think the economic story will be a plus for David Cameron. And running the referendum and winning it on Scotland was a plus. People said at the time it was a gamble, but, in the end, there was a 10-point difference, so that kept Scotland in the United Kingdom.

But his legacy inevitably is going to one which is colored by the fact that he took something of a gamble in organizing this referendum because his own party had become somewhat ungovernable, believed that he could win if it came to the referendum actually being held. And alas for him and alas for, in my view, many of us, it didn't work out.

And so the United Kingdom is leaving, and I think that the United Kingdom's decision to vote to leave the European Union is inevitably going to be one of the main features of David Cameron's political legacy.

GWEN IFILL: Former British Ambassador to the United States Peter Westmacott, thank you very much.

SIR PETER WESTMACOTT: Thank you.