“The strongest protection should be given to London’s Metropolitan Open Land and inappropriate development refused, except in very special circumstances, giving the same level of protection as in the Green Belt. Essential ancillary facilities for appropriate uses will only be acceptable where they maintain the openness of MOL.” (my italics)
from the Mayor of London office : here , London Plan Policy 7.17 on Metropolitan Open Land
assigns the same degree of protection as Green Belt
Another link from CPRE: Open Season on London’s Protected Green Spaces
In practise, check that your green space is still green space on the Local Plan; remembering that it can be built on “for the greater good”, such as schools. The development might have strong local opposition and be refused locally but is very likely to succeed on appeal to the Mayor or the planning inspectorate in Bristol.