Essentially, unless you hold an Air Operators Certificate (AOC), are a Flight Training Organisation (FTO) or fly a stupidly large number of movements a week AND can prove a legitimate case for the issue of a callsign, you will have "buckley's" chance of having one issued.
I know for a fact that formation flying by private individuals not operating under an AOC does not warrant the issue of an individual callsign. You should continue to use the registration of the lead aircraft and add the word "combine" or "formation" e.g. (G-ABCD Combine or G-CD Formation).
The availability of callsigns is in the same situation as radio frequencies in that there are precous few approved callsigns left in the world to be allocated. ICAO are responsible for the issue of all callsigns. In the UK, NATS merely screens the applications and forwards those that meet ALL the criteria to ICAO.
If you use a callsign for which you are not authorised, you will be in breach of the terms of your Flight Radio Telephony Operators Licence, and the Aircraft Radio Licence.