That,by it's condition,looks like a .303 round,and possession of such ammunition,without the appropriate authority,is an offence carrying a possible 5 years...although you would have to be up to other things,to cop for that.
Best to chuck it in the drink,as handing over will entail a bus load of questions,none of which you can shrug off.
DO NOT be tempted to "tap" the primer,as,unless it is held,similar to how a breach functions,the likely outcome,is a piece of the brass cartridge case,will embed itself in your person!