Mr Coulter died after being shot in the head as he and a friend left Jerky Chicken restaurant in Walham Grove, Fulham.
The Met said "it would appear the gunman had been lying in wait" for the pair to return to their car.
Detectives believe the gunman made off on foot towards North End road after shooting Mr Coulter.
The victim was shot as he was getting into the front passenger seat of the silver and black Renault Captur.
No arrests have been made.
A post-mortem examination has been arranged for Thursday.
Det Chf Inspr Noel McHugh said Mr Coulter's murder had "shocked the local community".

The off-duty officer suffered serious leg injuries in a booby-trap car bomb near Castlederg, County Tyrone.
The accused has also been charged with causing an explosion likely to endanger life or cause serious injury to property and membership of a proscribed organisation.
He is due to appear before Strabane Magistrates Court on Thursday.
A 44-year-old man arrested on Wednesday remains in custody, while a 37-year-old man has been released unconditionally.

Officers are investigating whether one of the men fell from a 12th floor balcony of the 19-storey Donside Court, in the Tillydrone area of the city.
Emergency services were called to the building at about 20:15 on Tuesday evening.
A witness has described hearing a woman screaming "help me, help me" before police arrived.
Police Scotland said it believed the incident was contained and there was not a threat to the wider community.
A blue forensics tent had been erected inside a police cordon at the foot of the building, close to the main entrance.
An eyewitness said they saw a man fall from the 12th floor of the building, which police confirmed they were pursuing as a line of inquiry.
Another witness, Toni Dey, 19, who lives a short distance away in Gordon's Mills Road, said she heard screaming from the block.
The mother of two said: "I heard some girl screaming 'Help me, help me', then about 10 minutes after I heard loads of screaming and shouting.
"I didn't call the police as I thought it was kids messing around, then I heard loads of police.
"It's very scary to think that something like that had happened. All I kept thinking was 'Why was that poor girl shouting help me?', and about a two-minute walk out my back door.
"I just moved in here in May and it's been so quiet. I was shocked to hear anything as I never normally do."
Another woman told BBC Scotland that she had known one of the men involved, describing him as a "nice boy".
Det Supt Dave McLaren said further information about the incident would be released in due course.
"At this time the investigation is in its very early stages," he said.
"However, the circumstances as they present at this time would indicate that this is a contained incident and we are not looking for any other person in relation to the deaths."
Police dismissed reports on social media that a police officer had been injured and said there was no suggestion the incident was terrorism-related.
Neighbour Susan Smith said police initially went up to the flat carrying what looked like a battering ram.
"There were loads and loads of police cars. I've never seen so many police cars. Four ambulance vans," she said.
"They took a lassie out and they were still trying to give the guy CPR. Then they put a tent up and the next thing forensics arrived.
"The police actually went in with a great thing like a battering ram at one point. Then they went in with stretchers and a chair thing - and came out with them empty."
Councillor Martin Greig, chairman of Aberdeen Community Safety Partnership, said: "There will be families grieving profoundly at this terrible news.
"Our sympathies are with those who have lost loved ones.
"The local community and the city will share feelings of shock at this violent incident."
Detectives investigating the murder of a 24-year-old man shot in a suspected ambush have named him as Salim Coulter.
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