Can you change the tank but leave the old one is it in the loft? As long as there is no damage to the tank it is better left alone. Don't be tempted to break it up to remove it.
It could be removed whole and your local council will be able to tell you where to dispose of it safely. I was able to dispose of some asbestos via my council by wrapping it in double plastic , and placing in a special skip, wear gloves and a mask that you can buy from a DIY store when moving it.
There are different types of asbestos and still a lot of it about in houses, get some facts and don't be scared of it, it may not cost you a lot of money to dispose of it, maybe just a little preparation and investigation.
Your council will also most likely have a specialist in asbestos removal who you can consult with.
Private companies can get involved but they will be expensive.
Finally are you certain it is asbestos this can only be proven by looking under a microscope at fibres.