OK, not the answer I was expecting from you.
The Highways Authority (which on the type of road you describe means the local council) maintains a statutory list of public roads and the documentation forming the 'legal' aspects of the extent of ownership. However the establishment of public highways have been ongoing since the middle-ages, so the extent of records and the process by which the road and its verges ends up as being regarded as 'dedicated to public passage' is variably. Sometimes the only course of action to establish ownership where there is disagreement is by legal case such that a judge decides. This is probably not what you have in mind, but there are a bunch of steps you could take by doing the donkey work yourself to find out the legal process and extent of documentation in your case.
Publicly maintained highways are created in one of four ways:
by history if the road was established prior to 1835, a key date
by specific dedication by the owner or by conveyance to a Highways Authority
by formal adoption
by acquisition under the '20 year rule' of general public usage of a route over a private piece of land.
It is my guess that yours falls in category 3. You don't say whether the houses constructed in the 50s where council houses or not. If they were, the council would have had to buy the land (or demonstrate prior ownership), including the access route to the public highway. If not, the same applies to a private developer. Whatever the method of build, the adoption of the public highway occurs as a separate process after the constuction of the estate. The relevant act now is Section 38 of the Highways Act 1980, however your estate was built prior to that.
There's a gap in my knowledge here, because I don't know the basis under which pre-1980 roads were covered in minimal legal documentation, for this Highways Act to apply.
You should start by asking the Highways Authority to provide the relevant documentation under s38 Highways Act 1980 for the extent of this road. You will have a pay a search fee for this.
Alternatively, if you know the houses were built by a private developer, you could try going back through the Land Registry records for one of the private houses on the estate (it doen't really matter which one since they should all hold similar reference conveyance information) looking for the original land conveyance (it should be a held file for reference under the Land title of the parcel of land) that transferred the ownership of the whole plot of land including access road in the first place.
Lastly you should know that a highway, once dedicated, including its verges, cannot be 'claimed back' by a neighbouring landowner under Adverse Possession.
I know Cassa is trying to be helpful; but her comments are irrelevant to this situation, whereby the question is one of extent of the width of the dedicated highway, including its verges.