The Rickie Lambert story makes for a better football film than many commissioned on the subject, even with a plot-line that stretches the bounds of credibility.

We have rejection by his boyhood idols at 15 and fighting back from the bottom of football’s pyramid while working in a beetroot factory to make ends meet. There is the symmetry of his personal redemption at a club seeking its own salvation, a Wembley winner on an international debut against the country’s historic rivals and finally – or the next chapter at least – rejoining those same boyhood idols as his parents dissolve into tears. It is a genuine football fairytale and it is hard to strip away the emotion attached to Lambert’s Liverpool transfer. Mercifully, Lambert has done that himself.

“There isn’t much sentiment in football and I don’t think this move is anything to do with that,” he said on switching from Southampton. He is correct. There can be no sentiment in Brendan Rodgers’ pursuit of that elusive Premier League title.

Lambert is not the marquee signing with the extravagant price-tag many would anticipate from a club aiming to make the small but monumental step from second to first in the Premier League. He is not the young, unpolished gem that Fenway Sports Group, Liverpool’s owners, have usually targeted since Rodgers became manager two years ago. There is little resale value in a 32-year-old nor is he an obvious choice for a Liverpool frontline blessed with phenomenal pace. And yet Lambert’s arrival makes sense on several counts for Liverpool.

For £4.5m plus add-ons (Champions League appearances, trophies etc) the club has acquired an England international with a proven Premier League record of goals and assists – a player who scored or assisted 23 of Southampton’s 54 league goals last season. It is simply a bonus that his allegiance is unquestioned and that his release by Liverpool 17 years ago sparked a mission to prove people wrong, one that has not slowed with Championship, Premier League or even international recognition. On top of that he has been signed early.

Lambert was the joint-fourth highest scoring English player in the Premier League last season alongside his new captain, Steven Gerrard. Top of that list was Daniel Sturridge, another new team-mate. There are now six Liverpool players in the England World Cup squad and Rodgers hopes to make it seven provided Southampton relent on their refusal to sell Adam Lallana for £25m. The Liverpool manager may be cornering the market in a pool of talent with low expectations in Brazil but the rapport they develop is to the benefit of a coach with firm belief in British players.

Liverpool had the Premier League’s finest two forwards in Sturridge and Luis Suárez last season. Beyond that, however, there was only Iago Aspas, the 26-year-old who struggled to adapt to English football and is available for transfer 12 months after his £7m arrival from Celta Vigo. Rodgers had few match-changing options available on the rare occasions Suárez’s or Sturridge’s contribution dipped during the title run-in, or when Liverpool ran out of patience in that defining home defeat by Chelsea.

“The late twist of fate will not be lost on Rodgers” was one of the Guardian’s five talking points from that game, focusing on Aspas’s meagre contribution compared with that of the Chelsea substitute Willian, one of the many who escaped Liverpool’s transfer clutches last summer. In Lambert, the manager now has proven support for his formidable forward line, not a risk in need of time and opportunity to develop.

Lambert will require patience in competition with Suárez and Sturridge for a first team place at Anfield. That can test any player accustomed to a regular starting role, even one who has sealed a dream transfer, although the added demands on Liverpool next season as Champions League qualifiers increase the prospect of rotation. The striker’s wide-ranging experience should also help.

“I think I am prepared mentally now for almost anything,” he said on becoming Liverpool’s first signing of the summer on Monday. “I’ve had a long career, I’ve experienced a lot – a lot of ups and downs – and I believe I am at a time in my life now where anything that happens, I can enjoy, get the most out of it and adapt to it.”

As for his role in Rodgers’ plans for next season, Lambert added: “He knows what the club means to me. I think he sees what he can benefit from by signing me and he knows I’ll be trying my best every minute I play for this club. I’m not sure what role he has for me – he hasn’t gone into great detail right now – but I will be speaking to him very shortly.”

Lambert’s signing signals a departure in transfer policy for FSG, who did not back Rodgers to the hilt when he wanted to sign Clint Dempsey, 29 years old at the time, from Fulham in 2012. It underlines what the manager’s new contract has already confirmed. They have no cause to doubt him now.

There is also a managerial shift evident in the striker’s transfer. Rodgers stated frequently during his first two years at Anfield that plan B was to make plan A better and now he clearly has a different problem to pose opposition defenders, although it is a gross exaggeration to suggest that Liverpool will change their style because of Lambert. Southampton were not exactly an aerial, wing-hugging team under Mauricio Pochettino and Lambert’s touch, creativity and range of goals have often been overlooked, though not any more. He is back under the fierce Liverpool spotlight, which is the only place he has ever wanted to be.