Hang out the flags, stock up the fridge, buy a new television and begin praying that Andros Townsend's metatarsal holds up.

Roy Hodgson wore an expression that was one part delight to three parts relief as his England side overcame Poland 2-0 on Tuesday night in a breathless encounter at a rowdy Wembley to qualify for next summer's World Cup in Brazil.

"Emotions are churning around inside me. I died a thousand deaths every time they crossed the halfway line," said a visibly relieved Hodgson afterwards.

If a week is a long time in politics, it is an eternity for an England football manager. Less than seven days ago, a jittery public feared Hodgson was on a spiralling trajectory to join Graham Taylor and Steve McClaren on the list of lampooned England managers who have missed out on major championships.

A sequence of dour results in eastern Europe culminated in a miserable goalless draw in Kiev last month.

But all that was forgotten amid a burst of enthusiasm for the verve, youth and energy on show in defeating Montenegro 4-1 on Friday and banished entirely by Tuesday night's victory.

Five minutes before halftime, echoes of 1973 – when England failed to beat Poland and did not qualify for the 1974 World Cup – hung in the air. A series of chances had gone begging and tension was building, but then Wayne Rooney nodded in a Leighton Baines cross.

The Manchester United striker, the one-time great teen hope of English football who spent the summer scowling at the centre of a protracted transfer battle, wore a beaming smile. Following a nervy second half, captain Steven Gerrard sealed victory with three minutes to go.

"Since I made my England debut, there's always been criticism from outside but it makes you stronger and under tremendous pressure we proved we could perform," said the Liverpool midfielder.

Despite the presence of more than 18,000 noisy Poles in the capacity crowd that made it feel more Warsaw than Wembley at times, England finished top of their qualifying group and milked the applause at the final whistle.

Again fielding a youthful, attacking side, there was a verve about an England performance in which Tottenham Hotspur's Townsend was again a revelation.

No one will be fooled by a home victory over a side ranked 65 in the world, particularly given a nervy second half.

Yet on the same night as West Ham's promising Ravel Morrison scored a sublime goal for the under-21s, the enthusiasm engendered by back-to-back victories will see hope spring eternal once more.

Admitting before the match he was far from Churchillian in style, Hodgson nevertheless tried his best to banish the ghosts of previous failures. The 66-year-old can now begin preparing for the draw on 6 December in Costa do Sauipe in the Brazilian state of Bahia.

He won't need reminding that his predecessor, Fabio Capello, headed for South Africa in 2010 after dominating the qualifying group but returned to bewildered boos as his side suffered from a familiar cocktail of nerves, injury, fatigue, overhype and underperformance as England were thrashed by a youthful German side in Bloemfontein.

There was also relief for Greg Dyke, the new Football Association chairman who began the job with a warning that England faced a rapid slide into irrelevance unless urgent attention was paid to the lack of homegrown talent in the Premier League.

David Cameron was quick off the mark in congratulating Hodgson's side. "Proud to see England qualify for the World Cup in Brazil," the prime minister tweeted.

Dyke knows a good World Cup run will do more than any taskforce to galvanise the country behind the national team.

However the travelling band of supporters who follow England across the globe is liable to be smaller even than the 10,000 who went to South Africa in 2010. Fifa, in their wisdom, have failed to locate the group stages in geographic clusters, meaning fans will have to criss-cross the country at huge expense to follow their team.

Nor is it entirely clear what they will find when they get there.

In June protests enveloped the Confederations Cup, the traditional World Cup dry run, as millions of Brazilians took to the streets to protest against corruption and under-investment in public services.

Yet most expect the fervour for football in Brazil to overtake lingering concerns over construction timetables.

Hodgson's secret weapon may be lowered expectations. Dyke has already written off England's chances and the manager furiously downplays them.

"We've got a chance. If you want to win the lottery, buy a lottery ticket. We have our ticket," he said after the 2-0 win.

For now, both can breathe again, contemplating a gala dinner on 26 October to celebrate the FA's 150th birthday that will now be a celebration not a wake.