Your solicitor will look into all this, if you get that far. No-one would expect you to know the legal position before you put an offer in.
Just because a road is unadopted, doesn't mean it isn't owned by someone. You can find out who owns it at the Land Registry. Their title register for the road will likely say it is subject to other plots of land having a right of way in exchange for contributing towards the upkeep. No contribution, no right of way (although that can be hard to enforce).
If the road is unregistered, ie ownership not known, there is a presumption that everyone along the road owns the bit of road in front of their plot up to the middle line. You can maintain your own bit if you like, but other owners will likely have a right of way due to having used it for a couple of decades or more.
The landlords on the street might not mind contributing to upkeep (possibly no-one has asked/volunteered to coordinate it) as they would be able to make it a business expense, I believe.
The council might adopt the road, this can be applied for, but they would want the road firstly put into an 'adoptable standard' by the road owner.
As above, if the road is unregistered, each plot owner along it is presumed to own a bit of it and could apply to the Land Registry to register it. It might also be possible to form a management company to collectively own the road, if it isn't ever going to be adopted.
A solicitor is best placed to advise on this particular situation, but this alone wouldn't put me off personally if everything else about the house was positive.