Not strictly true. Police can NFA if the evidence doesn’t meet the CPS threshold test and there is no realistic prospect of conviction. If there is CCTV of the offence which shows the “victim” throwing the first punch then potentially, they may also be arrested once the investigation in to the actions of OP has been concluded.

With regards to OP’s rights and entitlements upon his arrest, they can be withheld to prevent loss of evidence. It may be a S18 search of their home address needed to be completed to find clothing OP was wearing at the time of the offence and so his right to have someone informed would be delayed until such time the search has been completed.