England move from the potato field formerly known as Murrayfield to their home at Twickenham, a site that before being bought by the Rugby Football Union in 1907 was used to cultivate cabbages, for the next two rounds of the Six Nations. The venue for next year's World Cup final will be the location for 11 of their 18 Tests before the start of the tournament and their fixtures against Ireland, next Saturday, and Wales in the next round will provide an acid test for the hosts.

Twickenham is not be as impregnable as it was in the buildup to the 2003 World Cup, won by England – they went into that tournament having won 22 consecutive Tests at headquarters – but the men in white do not lose there often, and when they do it tends to be by a single-figure margin. Australia, New Zealand and South Africa have won at Twickenham in the Stuart Lancaster era, but the first two southern hemisphere giants have also lost, while the only side to triumph there in the past three Six Nations was Wales in 2012.

Even though England have only two home matches in this year's championship, two victories would be a significant landmark. In cabbage terms, the green of Ireland and red of Wales have done so much better at Twickenham than any of the other teams involved that the last time home advantage was made to tell against the Celts in the same campaign was back in the days when the only question asked about visiting sides was how many they would lose by.

Not since 2002 have England defeated Ireland and Wales at Twickenham in a campaign and, in the past 10 tournaments, they have been responsible for five of England's six defeats at home: the Irish in 2004, 2006 and 2010, and the Welsh in 2008 and 2012. The defeat 10 years ago ended a run of 14 consecutive home victories in the championship at the ground.

Back then, England did not just beat Six Nations opponents in front of their own supporters, they tore them apart. Wales conceded 156 points in their three matches during the period, Ireland 130 and Scotland 107; Italy leaked 120 points in their two visits and even France went for 48 in 2001. Lancaster's team are emerging from the stage where judgment is based on victory rather than the manner of it: the 20-point win at Murrayfield last Saturday over unexpectedly passive opponents prompted introspection rather than celebration.

"We let Scotland off the hook too many times and did not convert many opportunities into points," said the England captain, Chris Robshaw. "We were in their 22 more than the scoreboard showed and we will not get as many chances against Ireland. We are in a pretty good place after the first couple of games and we now have two matches at Twickenham. We are desperate to put on good performances for our supporters."

England's biggest Six Nations victory in the Lancaster era came against Ireland two years ago – 30-9 – just beating the two 20-point margins over Scotland this year and last. Four of that starting lineup are likely to take the field next Saturday – Owen Farrell, Dylan Hartley, Dan Cole and Robshaw –with one of the bench that day, Mike Brown, featuring in match-day squads this year.

There has not only been a turnover of players in the past couple of years, but a change in emphasis, and while England still have the capacity to take on teams at forward, as they did in the London rain in 2012 to subdue the Irish, they have become more adventurous.

"Back then, our defensive energy was very high and we had a lot of enthusiasm, but we were lacking in understanding and execution," said the flanker Tom Wood. "We are getting to the stage where our attacking game is improving, along with our general shape, and as individuals we have a much better appreciation of given situations and our relationships in the team, such as reading each other's body language and everything else. We are getting a better knowledge of one another. I came off the field in Scotland really disappointed because we left at least 15 points out there: we need to get everything right against Ireland."

Owen Farrell personifies England's burgeoning confidence. One of his predecessors in the fly-half jersey, Rob Andrew, once said that it took 20 matches to come to terms with the demands of international rugby. There was something mechanical about Farrell up until last autumn, adept at implementing a gameplan, but slow to react to what was in front of him. His try against Australia, exploiting a defence that was drifting across, expecting him to pass rather than run, was a seminal moment for the young Saracen.

"Owen's getting a lot more support from Billy Twelvetrees now," Lancaster said. "That second person organising the back-line is taking some of the pressure off him and it gives us a two-sided attack. Another thing is the influence that Mike Catt [the attack coach] and his dad [Andy Farrell] are having on him. Mike is getting him to do lots of work on scanning, seeing space and varying the speed at which he runs to the line.

"Owen used to be 100mph in defence and attack, but he is a lot more composed now and is seeing the picture unfolding a lot more clearly. The line-break he made just before half-time at Murrayfield, when Luther Burrell nearly scored a try, was a good example; he is getting players running good lines off him and, after doing a show-and-go, he went through and slipped Luther the ball. His general game management – when to kick and when to pass – has improved. It is down not just to experience, but design."

Ireland will challenge England's attacking intent, not just with a pack capable of dominating possession, as they showed against Wales when they backed up strong set-pieces by ruling the breakdown, but a wealth of know-how behind, where their triangle of Jonathan Sexton, Gordon D'Arcy and Brian O'Driscoll is one of the most experienced in international rugby.

England are chasing a first Six Nations hat-trick in the fixture since 2000 and it is more than three hours since they conceded a try to Ireland. More than that, they need to fortify Twickenham against the storms that will blow in during the World Cup. Ireland's next visit after Saturday will be on 5 September in 2015, the final game before the start of the tournament less than two weeks later.

"We are a difficult side to play against home or away," Lancaster said. "Our defensive work-rate, organisation, line speed, commitment and drive to work hard for each other make us hard to beat anywhere. Other than Wales last year, we have not been beaten by more than 10 points in 20-plus internationals.

"We are at the opposite end of the scale to Ireland in terms of Test-match experience, but we are not daunted because we have self-belief."