Definitely keep the ammunition in a separate bag and if possbile keep both bags secured so that neither can easily be opened, if you are concerned about getting about getting stopped it might be worth having the purchase receipt for the rifle with you, that way you can prove where you've bought it from.
If you are stopped or encounter a police knife arch, you are carrying the rifle in a responsible manner, it is not easily accessible and you have legitimate reason for carrying it under the Offensive Weapons Act, so the police won't have grounds for confiscating it or charging you.
In my experience of carrying swords on public transport if you are behaving in a sensible manner and the rifle is wrapped you won't have any problems.
Raven