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It could be both your land and a public highway. If it's a public highway maintainable at the public expense then the road surface itself will be owned by the local authority which is the relevant highways agency, but you'd own the subsoil. If it's a public highway but not maintainable at the public expense then you'd own the land entirely but it would be subject to public rights of way. The local authority will have a map showing what areas of land they consider to be highways maintainable at the public expense (usually described as a List of Streets). Often available online. It might be worth digging out a copy.
If you were parked on your drive though it would be surprising if that formed part of a public highway.
Anyway, Land Registry plans should not be relied upon for determining boundaries due to the general boundaries rule in rule 60 of the Land Registration Rules 2003.
On Christmas Eve we got a parking ticket for parking at the front of our house. There is a double yellow in front of the property and then our drive/front garden. We disputed this showing the land registry has the boundary of our property right up to the road but the council have come back saying it is a public highway. Any ideas?