Detectives believe a white man, in his 40s with blue eyes, has carried out all the attacks over the past year.
The majority of his victims are girls, with the youngest aged eight, and the rest are young women.
All were attacked during the morning or afternoon rush hours in south London.
Police have released CCTV footage of the suspect, which shows him running and walking near the scene of the latest attack on a 15-year-old girl in Sandbourne Road, Brockley, just after 8.30 am on 22 November.
In the video he appears to be slim with greyish hair and is wearing a dark coat and blue trousers or jeans.
Last month Sky News showed images of the man before and after an attack on a 25-year-old woman in Liskaerd Gardens, Kidbrooke.
At the time it was revealed he was suspected to have attacked three 11-year-olds in the south London areas of Grove Park, Lee and Forest Hill.
:: Police hunt suspected serial child sex offender in Greenwich and Lewisham
Detective Chief Inspector Andrew Furphy of the Metropolitan Police said: "These offences have been traumatic for the victims, all of whom have been young females going about their daily lives.
"There is a strong possibility that these incidents are part of a linked series of attacks as a number of victims have provided very similar descriptions of the attacker - a white man aged between 40 and 50.
"Our officers have been working tirelessly to apprehend the suspect, but we need the public's help.
"CCTV shows footage of a male that we would like to speak to who we believe may be able to assist our investigation. If this is you or if you know who this person is, please contact us."
Police believe there may be more victims who have not reported attacks and are urging them to do so.
The first attack is thought to have been on a 13-year-old girl in Orpington in October last year.
Most of the assaults have happened in the boroughs of Lewisham and Greenwich, but there have been others in Southwark, Bromley and Bexley.
Police said they had increased patrols in those areas and were advising schools and community groups.
Anyone with information is asked to call police or ring Crimestoppers, anonymously, on 0800 555 111.
:: The full list of alleged attacks that are thought to have been carried out by the same man took place:
At 9.15am on Thursday 6 October 2016 in Foxfield Road, Orpington BR8 [victim aged 13] - Bromley borough
At 4.30pm on Friday 28 April 2017 in Heathfield Lane, Chislehurst BR7 [victim aged 13] - Bromley
At around 7.50am-8.20am on Thursday 8 June in St Thomas Drive Orpington BR5 [victim aged 15] - Bromley
At 2.55pm on Wednesday 21 June in Springfield Grove SE7 [victim aged 18] - Greenwich
At 4.30pm on Wednesday 21 June in Heavitree Road SE18 [victim aged 16] - Greenwich
At 5pm on Wednesday 21 June in Lovel Avenue DA16 [victim aged 13] - Bexley
At 5.30pm on Wednesday 21 June in Plumstead Adventure Play Ground SE18 [victim aged 19] - Greenwich
At 8.20am on Friday, 30 June in Ravens Way, SE12 [victim aged 13] - Lewisham
At 5.20pm on Thursday 27 July in Falmouth Road SE1 [victim aged 19] - Southwark
At 8.50am on Monday 14 August in Kitto Road, Se14, [victim aged 27] - Lewisham
At 12.14pm on Friday 25 August in Green Chain walk, near Portland Rd, BR1 [victim aged 35] - Bromley
At around 1.14pm on Tuesday 29 August in Edward Tyler Road, SE12 [victim aged 11] - Lewisham
At 4.30pm on Thursday 7 September in Thicket Road SE20 [victim aged 28] - Bromley
At 5.20pm on Monday 18 September in Half Moon Lane SE24 [victim aged 11] - Southwark
At 8.20am on Wednesday, 27 September in Vicars Hill, SE13 [victim aged 13] - Lewisham
At 4.30pm on Thursday, 28 September in Frank Burton Close, SE7 [victim aged 13] - Greenwich
At around 8.15am on Thursday, 28 September in Alanthus Close, SE12 [victim aged 11] - Lewisham
At 9.20am on Thursday, 5 October in Kidbrooke Park Road, SE3 [victim aged 13] - Greenwich
At 9.30am on Thursday, 5 October in Kidbrooke Park Road SE3 [victim aged 27] - Greenwich
At around 9.54am on Thursday 5 October in Liskeard Gardens, SE3 [victim aged 25] - Lewisham
At 4am on Monday, 16 October in Honor Oak Road, SE23 [victim aged 11] - Lewisham
At 4.45pm on Thursday 19 October in Winn Common, SE18 [victim aged 14] - Greenwich
At Around 8.20am-8.50am on Monday 13 November in Vulcan Terrace SE4 [victim aged 8] - Lewisham
At 7.30am on Tuesday 21 November in Middle Park Avenue SE9 [victim aged 12] - Bromley
At 8.30am on Wednesday 22 November in Sandbourne Road SE4 [victim aged 15] - Lewisham