Although "bagsy" and "dibs" are the two terms I know best, another phrase that has a similar meaning is "two's up".
I first heard it on an episode of the UK TV show "QI" hosted by Stephen Fry. From the Transcript of Series 4, Episode 4:
Yeah. Yeah. [working class accent] "Two’s up on your burn."
Two’s up on your burn?
I swear I’m getting an erection.
I have to say when I first arrived in prison, I was a little discombobulated by the entire experience, as you can imagine; you have to give your finger prints and take your clothes off and it’s all very . . . It’s just like public school, it’s lovely. But the . . . the first person who came in; he said, "Two’s up." I said--[looks upward wonderingly]--"Is it? What? Where?" [working class accent] "Two’s up. Two’s up, mate. Two’s up. On your burn."
"Two’s up" means when you’ve finished your cigarette, you give it to the guy who’s first to say "two’s up" to you. And he gets the rights. It’s like saying "bags have your fag end," basically. And then they collect about six of those and then they make a new cigarette out of it.
And, from the Urban Dictionary, the currently top definition has:
Two's up is a very old Yorkshire expression meaning, "Save me a small amount of what you're currently consuming" It was originally used by miners who were hungry and wanted a piece of pie from one of their more fortunate colleagues. It became more popular in the 70's and meant "share your cigarette with me":
"I've left my fags at home, two's up on your rolly (hand rolled cigarette)"
And finally, the site ARRSEPedia (an informal, not 100% serious Wiki about anything connected to the British Army) has:
Popular amongst capwearing bus-stop dwellers, meaning to leave half of a cigarette for someone else. A chav equivilent of puting dibs on something.
(It should, perhaps, be noted that both the Urban Dictionary and ARRSEPedia include alternative, somewhat less salubrious, uses for "two's-up", although the meaning is broadly similar).