The Three Lions gave a first start to James Ward-Prowse and debut for Manchester City's Phil Foden, as manager Gareth Southgate targeted a winning start.
England looked to go ahead inside the opening four minutes of the match, but Harry Kane was unable to get the better of their opposing number with a speculative strike from 20-yards.
Kane did have the ball in the net two minutes later with a close-range finish from Raheem Sterling's in-swinging cross from the left, but it was disallowed for offside.
Iceland had their first chance of the match a minute after the half-hour mark through Hordur Magnusson, but the English dropped back to clear the danger.
In the second half, the Three Lions knocked purposefully for the opener but were met with a towering and bulky Iceland defence who evaded every threat.
Then, an in-swinging free-kick from Kieran Tripper 64 minutes in drifted narrowly wide of the far post with Hannes Hallordsson scrambling across.
Danny Ings entered to grab his second cap for the Three Lions three minutes later and first since 2015, with Foden making way.
England were down to ten players following the 70th minute after Kyle Walker earned a second yellow card for an off the ball challenge, as Mason Greenwood entered for his debut minutes later.
The Three Lions were given a lifeline after the referee pointed to the stop after Ingi Ingason handled in the area, leaving Sterling to send Hallordsson the wrong way.
Iceland were given an out of jail card a minute later as the man in the middle pointed to the spot again following a foul in the box, but Birkir Bjarnason was unable to capitalise- leaving the English to a winning start in the Nations League.