Captain Joe Root says his side have faced up to some "ugly truths" after a number of offensive historical tweets from England players were revealed.
Ollie Robinson apologised for racist and sexist tweets from 2012 and 2013 and has been suspended pending an investigation.
The England and Wales Cricket Board also said it will take action after tweets from others came to light.
"We want to move forward in a really positive way," said Root.
Speaking to BBC Sport before Thursday's second and final Test against New Zealand, Root added: "We've had to face up to some ugly truths this past week or so and there will be challenges moving forward.
"But the group of players we have now is very much committed to moving the game forward, to making it a better place, making it more inclusive and educating ourselves further.
"We're going to have to front up to what has happened, but ultimately we want to move forward in a really positive way, to keep going on this journey we've started of trying to better out sport.
"We will continue to do that because that's how we all feel."
The tweets from pace bowler Robinson, 27, posted when he was aged 18 and 19, were unearthed during the first day of the drawn first Test, whilst he was on the field making his international debut.
He later said he was "ashamed" and "embarrassed", and on Sunday was removed from the England squad while the ECB carries out an investigation.
On Monday, the governing body confirmed it was looking into a report by Wisden a second player had posted offensive material. The players' identity was obscured by Wisden because he was under the age of 16 when the post was made.
Then, on Tuesday evening, the ECB said it will take "relevant and appropriate action" after historical tweets from several England players were "questioned publicly".
Tweets by Eoin Morgan, James Anderson and Jos Buttler have been highlighted online.
This controversy comes after England began the first Test by sharing a 'moment of unity' with New Zealand, the home players all wearing T-shirts carrying messages of anti-discrimination.
Root confirmed England will make the same stance before the second Test begins.
"All we want to do as a side is keep trying to find ways of making it better, making it more inclusive, as diverse as we can, and a game for everyone," said Root.
"We've spent a long time talking about it - how we can make a change, how we can make a difference.
"As players at the top of the sport, we know that it's going to feed down from what we do. We're very aware of that and we're very keen to make change, and to take the game in a really positive direction."
On the field, England will look to protect a record that has seen them go unbeaten in home Test series since 2014.
In Robinson's absence, they will make at least one change, which will be influenced by the decision on the balance of the bowling attack - at Lord's, spinner Jack Leach was omitted in favour of four seamers.
If Anderson, England's all-time leading wicket-taker, retains his place, he will make his 162nd appearance and overtake Alastair Cook as England's most-capped Test player.
New Zealand will be without captain Kane Williamson, who is resting an elbow injury, but are set to recall pace bowler Trent Boult.
After around 6,500 fans were allowed each day at Lord's for the first Test, Edgbaston is set to welcome around 17,000 spectators each day.