You can apply to have the road 'adopted' by the council. However, councils always seem to be short of cash and they may look to the residents to contribute towards the costs. For example, this is from the Trafford Council website:
"Existing roads will not normally be adopted unless they are brought up to current standards by the owners of the road. It may for example be unpaved, without kerbs, footways, surface water sewers, gullies and lighting or any of these features, and its surface is probably in a bad condition".
However, the same page also states this:
"Under the provisions of Sections 205 to 218 of the Highways Act 1980, the highway authority, that is the Council, may resolve to raising the standard of a private street by providing any or all of the missing features or by improving the standard of any existing features. This procedure enables the Council on completion of necessary remedial works to adopt the street as a highway maintainable at public expense"
http://www.trafford.gov.uk/TransportAndStreets /RoadsHighwaysAndPavements/Roads-AdoptionAgree ments
It looks as if the only way you'll be able to get a definite answer about the possibility of your council adopting the road is by contacting the relevant department. With most councils it's probably still called 'Highways' but I notice that in Trafford it comes under 'Built Environment'. (Is there anything which doesn't get 're-branded' these days?).
Perhaps the first place to look might be the council's website?
Chris