Southwark Council has published a study, formulated by landscape architect Noel Farrer, that examines Burgess Park's future success.
The new document - Burgess Park: Time for Change - includes five priorities for the park, with details on how they can be achieved and the cost.
The priorities are: access to nature, demolition of existing roads and paths to create an extra hectare of green space, strengthening the boundaries of the park, creating unifying structures and art, and forming inviting entrances. The work amounts to £5.2m.
Along with Burgess Park, experts are examining another five green spaces across London.
The shortlisted spaces will compete for the Premier Park Award - part of Johnson's Help a London Park programme. The parks with the greatest chance of receiving the grant are Southwark's Burgess Park, Brent River Park, Haringey's Lordship Recreation Ground and Croydon's Wandle Park.
Also shortlisted are Fairlop Waters Country Park in Redbridge, and Mayesbrook Park in Barking & Dagenham.
Representatives from CABE Space, Natural England and the London Parks & Green Spaces Forum will advise the mayor on which park should receive the grant.
The Greater London Authority, London Development Agency and Groundwork London are also involved in the programme.
Southwark Council parks manager Jon Sheaff said Burgess Park's bid was part of wider funding applications, following the publication of Farrer's study.
"We have come up with a scheme that has now become the vehicle for funding applications of around £6m," explained Sheaff.
"We recognise we haven't got £20m to spend so we are looking at a scheme that puts in very basic infrastructure the park doesn't currently have."
He added that the aim was to create a park that people feel safe visiting, that is well cared for, that has a sense of place and identity, and that can be easily accessed. He said the work would focus on creating new entranceways.
The mayor's grant scheme also includes a public vote that will allocate a further £4m to 10 more parks in the capital.
A total of 47 parks have been chosen as candidates. The winners will be announced in February.
BURGESS PARK COSTS
- Demolitions roads/paths: £520,000
- Land swap/acquisition: £50,000
- Circulation path: £850,000
- New entrances:
- Old Kent Road: £550,000
- Camberwell Road: £600,000
- St Georges Way or Wellsway: £410,000
- Park entrance: £350,000
- Unifying structures/art: £900,000
- Tree planting: £600,000
- Biodiversity enhancement: £400,000