Among them are former National Trust director-general Dame Fiona Reynolds, architect Sir Terry Farrell, public health advisor Dr William Bird, Professor Michael Depledge, chair of Environmental and Human Health at University of Exeter Medical School, London Wildlife Trust chief executive Gordon Scorer, and Aecom director of sustainable development Ben Smith.
They say the move - which has been spearheaded by geographer Daniel Raven-Ellison - will improve Londoners' health, quality of life and environment.
"London being a National Park City would bring the greatest improvements in the quality of life in London since the clean-up after the great stink or since the Victorians started planting our great trees and beautiful public parks," the group said in a press release.
"Making London a National Park City is all about making our capital a healthier, greener and more enjoyable place to live. London has all the ingredients it needs to make this happen - the people, land, nature and expertise.
"All that's missing is the critical support of more elected councillors to give the National Park City a legitimate mandate. We hope that this letter will inspire councils and elected ward teams to declare their support for this potentially historic move."
The open letter has been posted to all ward teams that are yet to declare their support for London to become a National Park City. All candidates for the London mayoral campaign have given their support.
THE FULL LETTER
"We need your support to make London the world's first National Park City.
"For London to be declared a National Park City, two-thirds of London's 654 wards and the Mayor of London must declare their support. 180 wards have already given their backing, but a further 256 wards are needed. As experts in health, education, conservation, business, culture and planning, we would like your help to turn this vision into a reality.
"The benefits are clear. From children's development to improved physical and mental health, active engagement with nature is key to a better quality of life for Londoners. Greener infrastructure can lead to cleaner air and improved flood protection. 47% of London is already physically green; its natural beauty, wildlife and cultural heritage are part of the capital's global reputation and attraction to visitors.
"Traditional National Park status in the UK aims to "conserve and enhance the natural beauty, wildlife and cultural heritage of the area" and "promote opportunities for the understanding and enjoyment of the special qualities of the park by the public". Why not take these aims and apply them to the whole of London? That is the essence of this initiative; to create a new kind of National Park - a National Park City. This has the potential to dramatically improve the way we experience and engage with this great city.
"A Greater London National Park City would not seek to appropriate any formal planning powers, and will not add new layers of bureaucracy. It would be a privately funded charitable foundation that far from being a drain on the public purse, would actually be a net contributor in a number of ways. It has the potential to ease the strain on our NHS, increase productivity, spur innovation and inspire new business activities.
"A National Park City would build on what is already happening, by linking existing actions and activities, sharing the things that work, inspiring new initiatives and engaging the public like never before. It would help to reinvigorate the relationship between people and place, helping us all make the most of what the city has to offer.
"We, the signatories to this letter, wholeheartedly endorse the positive vision set out in the Greater London National Park City proposal (see http://www.nationalparkcity.london/).
"According to research by Lancaster University 9 in 10 Londoners think that making London a National Park City is a good idea, and 8 in 10 think it is something that London's councils should support. It also features within key recommendations set out by the Green Infrastructure Task Force.
"Please join 180 council wards, and Sadiq Khan, Zac Goldsmith, Caroline Pidgeon and Sian Berry in supporting this shared vision for London. We need all councillors in your ward to unanimously agree to declare the support of your ward. To see which wards have already backed the campaign, and to add your ward's support please visit http://www.nationalparkcity.london/ward_support.
"Together we can make London a greener, healthier and fairer place to live. Together we can make London a National Park City."