Doyle, 46, is a partner at south Croydon talent and PR agency Grant Doyle Associates.
He was arrested on Wednesday (23 March) on suspicion of inciting racial hatred on social media, after the police said it was investigating "a number of messages". One tweet, which has since been deleted, read: "I confronted a Muslim woman yesterday in Croydon. I asked her to explain Brussels. She said 'Nothing to do with me.' A mealy mouthed reply."
Doyle retweeted a number of posts that were critical of his comment.
Croydon PR bigot (@MatthewDoyle31) says something dumb on Twitter. His reaction? Spout more baseless venom!— Alistair Cunningham (@Cunningham_UK) March 23, 2016
The story was picked up by most of the national press.
Doyle then continued to tweet, in many cases using offensive language.
Who cares if I insulted some towelhead ?? Really.— Matthew P Doyle (@MatthewDoyle31) March 23, 2016
Doyle was taken into custody at a south London police station and his flat was searched. He was later released.
A statement posted on the Met Police website on Friday says: "Following discussion with the Crown Prosecution Service, Mr Doyle is no longer charged with the offence and will not be appearing at court.
"Police may not make charging decisions on offences under Section 19 of the Public Order Act. There will be further consultation with CPS."
PRWeek was unable to reach Doyle for comment, but he has continued to express angst at the Met using Twitter, including retweeting messages from people supporting his reported proposal to take legal action against the force.
Could someone tell the Met that they are supposed to meet me at my flat at 9am to return my possessions AND it is not Bank Holiday Tuesday.— Matthew P Doyle (@MatthewDoyle31) March 29, 2016
You won't believe what the Police have just said to me.— Matthew P Doyle (@MatthewDoyle31) March 29, 2016