Neil Kinnock, the Welshman who was Margaret Thatcher's main Parliamentary opponent for much of her time as Prime Minister, had a reputation for long-winded eloquence.

Yet he summed up her style in four short words: "Just me! And now!"

Criticism such as this resonated strongly in Wales and of course Scotland, but I think it was overdone, and my view was shared by many English voters. Mrs Thatcher gained far more votes in her third General Election victory in 1987 than she had in her first, in 1979.

Her style was not one of strident selfishness. Her ideology was not one of crude individualism. Her two key achievements as Prime Minister show her to have been a brave and visionary leader.

First, she initiated the Northern Ireland peace process (an achievement for which she received scant credit). In 1985 she negotiated the Anglo-Irish Agreement. The key, and highly controversial, component in the agreement was that the Irish Government – the government of a foreign power – was to be centrally involved in the constitutional process, with a permanent secretariat in Belfast. So Dublin was not just to be consulted. It was to be at the heart of the process.

This was a remarkable concession of British sovereignty, and it infuriated many of her closest friends and allies. It was an act of great political courage, and she paid heavily for it. Her dear friend and supporter Ian Gow resigned from her Government. Leading Unionists vilified her, Peter Robinson accusing her of prostitution. Ian Paisley called her a Jezebel and Enoch Powell accused her of treachery and said she deserved only contempt.

At first her brave act seemed to backfire, as the Troubles got worse, not better. But although the Unionists reviled her for selling out, Sinn Fein, and the IRA, slowly woke up to the notion that negotiation was a feasible alternative to violence. Irish-leaning politicians in the US changed their minds about her, and decided she was serious about wanting an inclusive long-term solution to a centuries-old problem. She had shown statesmanship of the highest order.

Secondly, she helped to end the Cold War. She did this primarily by persuading her very good ally and pal, President Ronald Reagan of the US, that he had to take Mikhail Gorbachev, the coming man in the USSR, seriously.

Well before most diplomats in the West had even noticed Mr Gorbachev, she had marked him out as the coming man in the USSR; she understood that he was a real radical, a significant reformer. After his visit to Chequers, Mrs Thatcher flew at once to the US and in talks with President Reagan at Camp David she impressed on him that Mr Gorbachev was a man with whom he would be able to do business. Later she frankly admitted that even she had underestimated just how radical he was going to be.

Her other notable achievement was to end the excessive and undemocratic trade union power which had made Britain virtually ungovernable in the late 1970s. Legislation to end the closed shop and enforce strike ballots might not seem radical now, but they were inflammatory in the 1980s.

In persona she was less strident and less callous than the caricature of her as a hard-hearted harridan would have us believe. Two Scottish MPs, one Labour and one Tory, told me privately of very considerable personal kindness she showed to them.

When she visited The Herald offices in 1983, on the occasion of the paper's bicentenary, even her many detractors on the staff had to concede that her tour of the various floors of the old Albion Street offices was a triumph.

It was a late-night visit – she had been attending a banquet elsewhere in Glasgow and did not arrive until almost 11 pm, but she stayed for more than two hours – and most of those present, including the lady herself, imbibed plenty of whisky to mark the occasion. I had already imbibed rather too generously before she even arrived.

To win a bet, I kissed her hand when I was introduced to her. As I slobbered drunkenly over her proffered hand, she had the grace to look quite pleased. Arnold Kemp, the editor, said to her: "Harry is one of your admirers." I said: "Yes, we have terrible arguments about you." Not the most tactful thing to say, no doubt, but she laughed loudly, with every appearance of sincerity.

Later that night, one of my more hard-bitten colleagues, a socialist of the old school, reluctantly conceded: "I admit it, she's a star."