'You saw a weight come off our shoulders," Wayne Rooney said of the goal early in the second half that set England on the way to victory against Montenegro and kept their hopes alive of beating Poland at Wembley on Tuesday to qualify for next summer's World Cup as group winners.

The Manchester United striker was right. The second-half improvement was visible. Despite all the deserved plaudits for a bold attacking selection and what was, by the end, a convincing scoreline, the first half contained too much of the old England to inspire complete confidence of a similarly positive result in three days' time. It is another must-win game, for Ukraine are guaranteed three points against San Marino. Yet England often do play with a weight on their shoulders when they appear at Wembley and even Roy Hodgson acknowledged relief that Rooney's goal arrived at exactly the right time.

"It was a good win in the end, but it came after a first half where it wasn't looking that easy for us," the England manager was honest enough to admit. "If the game had gone on for another 20 minutes with us bashing our heads against the wall of defenders and getting nothing but corner kicks, who knows what the outcome would have been? But luckily that didn't happen, we scored at the right time. After that we played the type of football we wanted to play with the players at our disposal, and that is what got us the goals."

By virtue of their defeat by Ukraine on Friday, Poland have no active interest in their final game, the only remaining issue is who tops Group H and who ends up in the play-offs, but Hodgson and Rooney doubt whether the Poles will turn out to be pushovers.

"It's another massive game for us," Rooney said. "When you look at the two teams, Poland are probably better than Montenegro, much more dangerous on the counterattack. But we are all looking forward to the game, there is an excitement around the squad now. I think that showed against Montenegro and hopefully we can keep up the momentum against Poland."

Hodgson managed to watch the first half of the Ukraine game and was surprised Poland lost. "They played well against Ukraine, they were the better team in the first half," he said.

"I can't imagine they will take their foot off the pedal in the last game. They will want to come here and win, get a good result like Poland did in 1973. However they approach the game we have to be aware that they are usually capable of scoring on the counter, and respect the fact that in Robert Lewandowski and Jakub Blaszczykowski they have two of the top strikers in Europe."

The 1973 game, with Jan Tomaszewski proving himself to be not quite the clown in goal that Brian Clough had suggested, is bound to loom large in the next couple of days as a backdrop to an almost identical final group game against the same opponents, though the circumstances were somewhat different then.

England were denied by a goalkeeper having the game of his life, a 1-1 draw at Wembley ultimately costing Alf Ramsey his job and allowing the FA to inflict Don Revie on a nation that would have preferred Clough. But Poland went on to have their most successful World Cup in Germany in 1974. They finished in third place, Grzegorz Lato was the tournament's top scorer, and in Warsaw during the European Championship last summer, it was possible to buy T-shirts commemorating the day that Poland beat Brazil.

As England would probably not have achieved any of those things had they qualified at the Poles' expense, it is unfair to suppose that a freak goalkeeping exhibition was all that prevented Ramsey's players making the finals, just as Poland should not be seen as lucky underdogs.

England did not realise it at the time, but they were playing against golden-era Poland, and third place in a World Cup away from home is still better than anything England have managed, golden generations or no. Present-day Poland are good, but not that good. England should have beaten them in Warsaw last year, and, had they done so, they would have been in a more comfortable position approaching the final game.

As it is, England know what they have to do. They have to win, and to do that, they have to score goals, preferably fairly early in the game so that the weight of Wembley does not start to bear down on their shoulders once again.

Frank Lampard is not the first to make the observation that opposing players all tend to raise their game at Wembley, whatever is at stake, though what is more mysterious is why England so often shrink when playing at home. "Sometimes when it is 0-0 at half-time, you can feel people growing edgy, but this time the fans were very good and very positive," Lampard said. "That will build up even more for Tuesday and will help, but the onus is still on the players to go out there and do it."

As a veteran of the Croatia defeat when Steve McClaren's England were denied access to the European Championship six years ago, Lampard knows that patience is sometimes necessary in international football and that even the supposedly smaller nations often have a few quality players.

"Montenegro had a few, and so did Croatia at the time, though I don't want to dwell on that because we are looking to the future," he said. "I was happy to see such an attacking lineup against Montenegro, it helped us play on the front foot, but I don't necessarily agree that a cautious approach is always a bad thing. There are moments in games where you have to be cautious and you have to play with a head. People said Mourinho was cautious when he first came to Chelsea, and we used to beat teams regularly by four and five. People forget that. A good manager has to know how to set up in different situations."

A good manager must be a diplomat too, and Hodgson was able to get something off his chest after Friday's 4-1 win that had been bugging him for the past eight months. "I don't mind saying this now, but I was irritated in Montenegro last season when [the president of Montenegro FA] Dejan Savicevic suggested that English players just play for themselves, they don't care about the shirt," he said.

"Savicevic thought his own players did, they would throw themselves into everything. A complete load of rubbish in my opinion, but as we played badly in the second half and they got a 1-1 draw, I had to swallow that. He might be changing his opinion now after watching us swarm all over his players at Wembley. I think we have shown we have pride in the shirt. Every time we lost the ball we got it back very quickly. I was very pleased about that."

And was that, perchance, the half-time motivation Hodgson used to effect an improvement in the second half? "No, I didn't mention that to the players," he said. "It was only bothering me. I've just taken a cheap shot."