After the signalmen's strike in 1994, the company ranked in market research surveys as one of Britain's least popular businesses. "The dispute established a good brand name, but not a particularly good brand image," Mr Horton says, with deliberate irony.
The memory of the strike may be fading, and the fiasco of mistakes in the train timetable has been corrected in the January edition. But Mr Horton appears to be putting much thought into the reasons Railtrack, the company that owns the railway lines, the signalling systems and the stations, has taken such a pasting.
Mr Horton says: "It is a curious thing about our fellow- countrymen that though only 10 per cent travel regularly by train about 90 per cent have a visceral feeling for the railways and their part in our heritage. We have to understand the depth of emotion people feel about the railways."
The very public mauling he received at the time of the strike was perhaps a symptom of that, and it was certainly not all his own fault. Ministers were solidly behind Mr Horton's overhaul of Railtrack's archaic pay structures, some dating back to 1919, because without radical change the company would have been unsaleable on the stock market.
Mr Horton found himself the fall-guy in the front line, grilled by a parliamentary select committee and, worse still, roasted alive by the Today programme.
"I have no argument with John Humphreys [of Today] - he's there to kebab people and he did his best to. But I felt slightly bruised that the thing became personalised because I really genuinely felt - without being pompous about it - that I had come into this job to do something that would ultimately end up with a better railway."
Mr Horton insists it was absolutely right to "get rid of all those old Spanish customs, to produce a package for our employees that did not rely upon an elaborate Byzantine series of allowances and overtime".
Unpopular as the strike helped make rail privatisation, he takes a philosophical view. "One's shoulders are broad and history will vindicate what we are doing," he says. "I passionately believe that we cannot continue to cover our little island with tarmac, I really believe we cannot continue to pollute the atmosphere."
This, he admits, may sound curious for a man who spent 35 years in the oil industry (he was previously chairman of BP). But clearly anxious to pre-empt cynical reactions to his conversion, Mr Horton says he became a convinced environmentalist during his time running BP's US operations - a period that included rival Exxon's little difficulty with the tanker Valdez - and he cites his behind-the-scenes but influential work for the Rio summit on the environment as a credential.
Mr Horton says: "We have railways inherited from our Victorian ancestors, a priceless asset with 22,000 miles of track which has been woefully under- utilised and starved of investment for a long time."
Mr Horton says one reason Railtrack has been on the defensive is that it has been restricted in what it can say because of delicate negotiations with the rail regulator and the Government. Most of the battles are now over.
The regulator agreed on Friday that Railtrack could keep 75 per cent of the profits of property development. Tomorrow's interim results will show how the warring parties have resolved a complicated argument over the performance regime set by the rail regulator, John Swift.
This will penalise Railtrack heavily if it misses targets on the timeliness and reliability of services it provides to train operators, and reward the company if it beats them.
Mr Horton describes the outcome as "rather like a magistrate saying I would have fined you pounds 50 but I know you can't afford it this year so I will fine you pounds 10 because the pain is just as great". The relief is nevertheless bound to be challenged by Labour as an expensive sweetener for the City.
The decision on access charges leaves one big issue to be resolved before the prospectus can be finished - the amount of Railtrack's pounds 1.7bn debt that will be written off ahead of the flotation. Mr Horton refuses to talk about the numbers or the negotiations, but says it will have to be resolved fairly quickly. "A lot is turning on that."
The higher the debt, the harder it will be to raise capital to finance future investment, which Mr Horton has promised will be at least pounds 1bn a year. If the Government decides new projects such as Thameslink 2000 are to go ahead, the Treasury will almost certainly agree to write off more debt to help Railtrack afford the work. The City thinks the pounds 1.7bn might be halved.
Once that is settled, the pitch to professional investors will be simple. Mr Horton says: "We will be saying that we have here a regulated utility whose forward income for the next five years and initial cost base is fairly well known. Two-thirds of the costs are contracted for, and those contracts will be exposed in the prospectus. You have an interesting company with a stable, essentially non-cyclical, income stream . It will have - to start with at any rate - a small supplementary stream of property and retail income."
As for private investors, who are to be offered at least 30 per cent of the shares, Mr Horton hopes to exploit that love-hate relationship among the public that has made life so difficult for Railtrack. Buyers will be urged to own a part of "their" railways.
He says: "Over the next few months we will make a concerted effort to explain the real benefits of privatisation. We need a better rail system, and that means we will have to be more reliable, more punctual, with cleaner trains and stations that are a pleasure to be in and travel through." The sales campaign will be announced in a month and will be aimed at more sophisticated investors than the Sids who brought into British Gas.
Privatisation will, Mr Horton hopes, begin a virtuous circle of investment, falling costs and rising customer numbers that will allow the costs of travelling to fall.
He believes the rail franchise companies will soon begin to press him for significant changes in the way Railtrack operates, to fill their trains.
For example, he foresees an end to the ritual weekend maintenance programmes that disrupt timetables, send trains on long detours on Sundays and deter customers.
If the franchisees wanted an end to Sunday maintenance "my answer would be 'delighted, let's talk about how we can do it'." The work could be done at 3 am if need be, he adds.
But with the first private franchises not due to start formal operation until next month, the prospectus will take a cautious line on prospects. "We are not going to promise what we can't deliver," Mr Horton says.