There has been a good deal of work done, essentially the conclusion is that any solution can be made to work, but there will be potential impacts to other airports operations.
Tfl and Davis commission websites publish the detail when it is accepted. Here is an example of early work involving NATS:
The CAA FAS plan is also worth a read:
https://www.tfl.gov.uk/cdn/static/cm...ats.pdf’
http://www.caa.co.uk/docs/2408/FAS%2...ent%20Plan.pdf