When Phil Spector released the album a Christmas Gift For You he was hoping, no doubt, for a decent level of publicity and an early sales boom. But November 22 1963 - the release date - also happened to be the day that President John F Kennedy was shot. So it was Spector's misfortune to see his album launched just as American shops closed for a period of mourning and into a market place that wasn't in the mood for celebrating. His album was completely overshadowed.

Alastair Cook could, to some extent, empathise. Despite producing his finest innings since the tour to India in late 2012, Cook's contribution was largely overshadowed by the brilliance of Ben Stokes, who thumped the fastest Test century ever seen at Lord's. Cook's face won't be the one smiling on the back pages of papers in the morning. He is the man who caught a salmon the day his friend caught a mermaid.

It is not that Cook won't be admired. It is just that Stokes' skills are the more marketable. Spectators can come to rely on Cook; they can fall in love with Stokes.

Cook is used to such things. He was, after all, at the other end for much of the time when Kevin Pietersen played perhaps his greatest Test innings - the majestic 186 in Mumbai in 2012 - and saw his own accomplished century reduced to a footnote in most reports. He knows he is more supporting actor than leading man. More Felix Leiter than James Bond. But he didn't mind then and he won't mind now. For Cook will know that his century laid the platform for Stokes' brilliance. And he will know that the combination of their talents has given his side a chance to win a Test that looked lost only a few hours earlier.

There was nothing soft about this innings. The match situation was testing, the bowling was excellent - it is hard to think of a pair of new ball bowlers more suited to early-season England than Trent Boult and Tim Southee - and the conditions, initially at least, hugely demanding. Yet he has, to date, concentrated for eight hours and 39 minutes without providing a chance. It was probably his best innings since the end of that 2012 India tour.

Ross Taylor accepted Alastair Cook and Ben Stokes "took the game away from" New Zealand on the fourth day at Lord's. England finished the day with a lead of 295 and four wickets in hand, with Taylor admitting that the Test had edged "in England's favour" and that Cook had played an "outstanding" innings. "Stokes was very good to watch," Taylor said. "He wasn't reckless, he was very controlled. I played with him at Durham. He was a very talented player then. Cook has been under pressure, but that was pretty much a chanceless innings. It's up with the best I've seen from him. His tempo and his concentration were outstanding." The last time New Zealand were here they were dismissed for just 68 in the fourth innings chasing a target of 239. But while Taylor reasoned that his side would "back ourselves to chase 330 on a good day," he admitted that "it is still not an easy wicket to bat on" and that England's spinner, Moeen Ali, would enjoy the rough created by Trent Boult, the left-arm seamer. Stokes, meanwhile, credited Cook for his support. "He held the innings together," Stokes said, "He allowed me to play the way I did. We owe a lot to the innings that Cook played today. I played on instinct. I played my natural game and he let me get on with it. "I was nervous in the 90s. Especially after missing out in the first innings. But it was just one of those days where everything went right and breaking the record and getting on the honours board here is very special for me."

Those hours spent working in the nets with Graham Gooch in the early months of the year have paid off. After 18 months when he appeared horribly fragile outside off stump, he has rediscovered a technique that allows him to leave brilliantly - the difference between him and Ian Bell in this Test - defend positively and pick off runs in "his" areas efficiently - off his hips or when the ball is short. It is a method that rarely raises the pulse or makes you purr or gasp, but like chlorine and fluoride and inoculations, its value might be most obvious if it was absent. He has now passed 50 seven times in his last 12 innings.

But there have rarely been many doubts about Cook as a Test batsman. While he endured a horrid run of form and was fortunate to survive in the ODI side for as long as he did, he had earned patience in the Test side through his performances up to the start of 2013 Ashes series. The questions have been more about his captaincy. And this innings does not, harsh though it sounds, do much to dispel them.

There are different ways to lead a side. Some, the likes of Mike Brearley, might be fine orators, or man managers. Some, like Imran Khan, are blessed with an ability to rouse and inspire with their words and performances. Cook does not have those skills. He will never be a great orator or tactician. He will never rouse with a speech and rarely surprise with a tactic. Instead he must lead by example. And, at his best, he does that very well.

Cook has had a few great moments as a captain; nearly all of them in India. One of them came in Ahmedabad, when his century in vain inspired his dispirited side into believing that Indian conditions - and Indian spinners - could be conquered. Another came before that tour started when he insisted that Pietersen be included; a move that spoke of admirable diplomacy skills and a fierce desire to win. But generally he has been, at best, a safe pair of hands as a leader. And if England feel that Joe Root is ready - and few people will know him better than Jason Gillespie, the man who fast-tracked his leadership career at Yorkshire - it cannot be long before he takes over. Probably in the UAE this autumn.

Cook's biggest problem may simply be that he is tainted by association with a toxic brand. His allegiances to an ECB regime that treated spectators in high-handed fashion, his elitist portrayal - for which he is not responsible - as one of the "right sort of people" that England captains should be, and his dogged insistence on clinging on to the ODI captaincy long after it became apparent that it was time to let go, have combined to damage his reputation. It has created a suspicion that he has a sense of entitlement. That his appointment is less based on merit than a feeling that he represents the old order. His latter failure to manage Pietersen - one of England cricket's greatest resources - is also a disappointment.

It may well not be a fair suspicion. There have been times when Cook's limitations have been magnified by a media that, in some quarters has something of an agenda and, in one high profile case, a lack of imagination to think of anything else to talk about. And it might be noted, too, that there were times on the fourth day here when Brendon McCullum looked bereft of ideas when trying to stem the flow of runs. Captains are often reliant on the quality of their players and there have been times when Cook has been let down by his senior ones, in particular.

It will be hard to arrest the momentum of the narrative that Cook is a poor captain. Despite this innings, he may still be judged negatively if he fails to time his declaration correctly or if he is deemed to miss a trick in the field. It has got to the stage where he can't win. But life isn't fair. And as the ECB look to win hearts and minds with a new-look side, it may well be that Cook is axed to allow fresh branding. It's not a good reason, but it is a reason. Stokes is the sort to reengage the public; Cook is ruined by his past.

Besides, Cook can be a leader without being a captain. He can play the sort of role that Jacques Kallis or Desmond Haynes or Justin Langer used to provide so often . This was the innings of a leader. It wasn't necessarily the innings of a captain.