what to do with an old garden hedge? (could be at least 160 years old)

I think only you can make that decision - if you like the hedge, then its worth tidying it up and trying to remove some of the bindweed and ivy, though this will be a never-ending task. If you hate it, then you might as well remove it, try to get rid of the ivy and bindweed and decide what else to plant.

May it have birds nests in it come spring?

Post photos? Then we could have some kind of aesthetic to consider.

A hedge 160 years old is a rarity and should be preserved, if at all possible. I guess that at the moment it is very overgrown and untidy? You might want to consider finding a local 'expert' who can visit you and give-hands on advice.

I agree 160 years is a lot of growing time to destroy in a couple of days Unless you really really need the space think hard before rooting it up, I'm sure you'll find advice on " laying" it properly somewhere on the internet. Do that and I think you will get agreat deal of satisfaction apart from anything else

my first question has to be....what age are you?? and i,m not being rude, i recently had the very difficult task of cutting down a 90ft long hedge which was 8ft high because i could not manage to keep trimming it, and have successfully with help from my friends built a 6ft fence in its place!! so basically what i,m saying casey 1 is if your young and fit and like your old hedge then keep it but i,m a firm believer in low maintenance, so i can enjoy the nicer parts of gardening. hope this helps and good luck. jintymac