The law relating to adopted highways (roads maintained by the Council or Highways Agency) and public rights of way (public footpaths, bridleways etc) can be very complicated (and my comments here are not comprehensive: they are very general guidelines but not a statement of the law). Very few roads are built on land owned by a local authority or the Highways Agency (examples could be motorways or new bypasses). It is usually the case that if you own a house adjacent to a road maintained by the council your property deeds will show that you own the land to a point about half way across the road and the property opposite will own the opposite side of the road. The complication is that the surface has a legal status of being 'Queens Highway' so your deeds may show that own the land but the reality can be that the a person, a horse, a bicycle, a car or any other mechanically propelled vehicle may have a right of passage along the surface (just who can use the route is determined by highway law). Many people do not realise that it is not the Council who pays for the construction of new roads when new estates are built, it is the developer who foots the bill for the cost of the new roads and this cost is part of and included in total cost of your new house. The developer has to have planning permission to build the new road and most importantly, if the developer wants the council to assume the responsibility of maintaining the road the developer has to prove that it has been built to specified standards.
Things can be a lot more complicated on rural lanes and it can often be the case that the land on which some of the very old roads are built does not seem have an owner. Before 1835 landowners were required to pay tax to the parish (a tithe) on all land used for agriculture. The complication was that horse and carts were already using tracks known as 'ancient highways' across or at the edge of the fields. The landowner said 'I am not able to use the strip of land used as a road for agricultural purposes and refused to pay tax (the tithe) on it by renouncing ownership. No one else would want this land because it could not be farmed if horse and carts used it as a through route. The tithes were abolished when the whole system of building and funding roads needed to be changed in response to the industrial revolution
Just who owns the land below the surface of the tracks to Roman Lakes I do not know: this could be found out by paying for a legal landsearch. I think that you can be pretty sure that it isn't Stockport Council. During the nineteen hundreds the Council assumed responsibility for the maintenance of many urban roads but a strange twist of fate was that some houseowners who lived in the wealthiest residential roads objected to the council building a surface on what was the private road to their properties because once the road was built by and maintained by the council every car owner irregardless of whether they were accessing premises on route could use it. These are now the very roads with houses which may have three or four cars in the driveway. If the residents now want the road to be maintained with a metalled by the local council they first have to get council approval and then share the costs of building the road between existing residents.
In 1949 the National Parks and Access to the Countryside Act gave walkers and horseriders the legal right to walk on existing footpaths or ride existing bridleways across private property (hence the term Right of Way) if the route had been used continuously used without objection from the landowner for the preceding twenty years The map of public rights of way is a legal document called the 'Definitive Map'. This map shows Lakes Road from its junction with Bottoms Mill Road to have the legal status of a bridleway. The bridge across the River Goyt is a public footpath which them goes up the side of the hill through the wood and across the railway to Strines Road.
Just what the way forward is for the Roman Lakes I really do not know. Vehicular access is difficult because of the width and weight restrictions on Low Lea Road at Marple Bridge. I am a voluntary Footpath Officer for Ramblers Association in another area but I think that I can safely say that Ramblers, Peak and Northern Footpath Society, Stockport East Bridleways Association and the Open spaces Society and many other environmental groups would fight any application to upgrade the route to encourage even more vehicles to drive in the valley. The area is one of Stockport's greatest assets and an upgrading of the road could lead to many more cars, possible housing development and ultimately the destruction of the beauty and peace of the area.
