England have built up a four-point cushion at the top of Group F but Gareth Southgate is not taking World Cup qualification for granted.
Jermain Defoe and Jamie Vardy efforts gave the former England defender a 2-0 victory over Lithuania in his first competitive match since being confirmed as permanent manager.
England are the only team in European World Cup qualification yet to concede at the halfway stage. Slovenia slipped out of second place after losing away to under-pressure Scotland, with Slovakia usurping them after beating rock-bottom Malta.
England are 1-33 with some bookmakers to win the group but Southgate is not expecting it to be so easy, especially with a trip to Scotland awaiting in June.
"The group is in our hands, which is the most important thing," Southgate said.
"We still have a lot to do.
"The home games (against Slovakia and Slovenia) are the important ones for us in terms of direct opposition in positions two and three at the moment.
"But we know what going to Scotland is going to be like and we have to go and play on a plastic pitch in Lithuania.
"There's still plenty to do and also we have got to keep looking to improve with every performance."
England's June 10 clash in Scotland is set to be as fascinating as it will be highly-charged.
Harry Kane, Daniel Sturridge and Wayne Rooney will be hoping to return after missing the friendly in Germany and the qualifier against Lithuania - absences that enabled Defoe to complete an unlikely international renaissance.
Devastated to have been overlooked for the 2014 World Cup months after heading to Major League Soccer, the 34-year-old's fine form for struggling Sunderland earned him a recall.
Defoe's strike midway through the first half capped an international return to remember and Southgate has opened the door to the veteran heading to Russia next year aged 35.
The England manager said there is no reason he would be overlooked if he is still scoring in the Premier League. Asked whether goals in the Championship - with Sunderland currently battling relegation - would count for as much, Southgate said: "I walked into that!
"I guess, going back to what I said in the week, the ideal world for all our players is that they are playing at a high level and playing regularly.
"The flip-side of that is we don't have a huge pool of players to pick from. We have to balance off a few different things.
"I can't constrain myself on selection entirely, but I know ideally what I'd want to have. His performances this season and his goalscoring form have counted for him."
Defoe was named man of the match at Wembley but Adam Lallana pushed him close.
England's reigning player of the year impressed again on Sunday, with his sublime ball to Vardy capping a fine display.
"Adam injects something," Southgate said of the Liverpool attacking midfielder.
"He created a really good opening just before the first goal.
"The game in tight areas is where his quick feet and quick brain stand out.
"It wasn't an easy game for us to press because as soon as you press it was going longer, so there weren't so many opportunities for us to turn the ball over high up the pitch and counter on it.
"He starts that press off and he's a player I am really, really impressed with in terms of his mentality and ability."