An outbuilding erected in the curtilage of a dwelling was occupied continuously as an independent dwelling for four years in breach of planning control. An application for a lawful development certificate (LDC) was applied for some years later. During the intervening period there was a break of more than a year when the building was still equipped for independent occupation but vacant. The local authority refuses to issue an LDC for use as an independent dwelling because occupation was not continuous during the previous four years. But I think the use has accrued planning rights that can only be lost through abandonment. I would be interested in your thoughts.
In the case you describe it does not seem to be disputed that at some time in the past residential use of this building had taken place on a sufficiently continuous basis to ensure that an LDC would have been granted had it been applied for shortly after four years had elapsed.
However, where an LDC is requested some years later and premises have been vacant for a period within the four years before the date of application, the judgement in Panton and Farmer v Secretary of State for the Environment and Vale of White Horse District Council  comes into play. Here it was held that lawful use rights notionally obtained in the past can only be lost by evidence of abandonment, the formation of a new planning unit or a further change of use.
The case introduced the concept of dormancy. Applying this test, it seems unlikely that the period of vacancy you describe would be critical, provided the premises remained suitable for and were intended to be made available again for separate residential use. A good appeal case parallel worth referring to is DCS Number 049-804-684.
A developer proposes to demolish two substantial houses with large gardens and build six new homes. A similar plot has just been developed in an adjacent cul-de-sac. This has taken two years to build and has caused considerable noise and disturbance to residents, particularly through the use of piledriving machinery. Could it be argued that residents have suffered enough recently from noise and disturbance and that further disruption is unacceptable? Also, could an argument be mounted on the basis that physical building capital, in the form of the existing houses, will be destroyed and lead to unnecessary use of additional energy, building materials and travel miles during the construction period?
On the first issue, construction noise can be a material factor in determining a planning application, although I know of no case where it has been upheld as the sole reason for refusal. It is normally reasoned that construction noise is an inevitable temporary manifestation of any development project and is not the concern of the planning system unless there would be exceptional harm to amenity.
Where this is the case, a planning condition restricting construction hours is often applied. In the situation you describe I think the principle of fair administration would reject an "enough and no more" stance because this would unreasonably discriminate against a developer who happened to come along second.
Your other point raises the issue of whether the demolition of otherwise sound buildings is a matter to be weighed in the sustainability balance sheet. In fact, it rarely arises as a planning consideration because normally the more efficient use of land brought about by redevelopment far overrides any argument that it is more sustainable to retain existing buildings.
It is also probable that the new buildings will be more energy efficient than their predecessors. The only relevant appeal case I have been able to identify (DCS Number 049-304-618) concerned a one-for-one house development where an inspector felt that this compromised sustainable development aims.
Following PD's query (Planning, 31 August, p21) relating to the scope of hours of construction conditions, my local authority has attached such a condition to a development. It requires that construction work shall not take place at any time other than between the hours of 7.30am and 5.30pm on Mondays to Fridays. Building work has commenced and occasionally delivery drivers arrive at the site before 7.30am and have to wait in a residential road. Does this breach the condition?
Since the condition refers only to "construction work", it cannot be reasonably stretched to control the situation that you describe. While it might have been possible to devise a condition that included reference to hours of delivery into the site, serious questions of validity would arise if its requirements were outside the control of the developer.
The early arrival of suppliers' vehicles and their legitimate parking off-site until the site is operative is hardly a circumstance over which a construction company would have any direct influence, unless it is using its own vehicles. The only resolution of this problem is for your council to ask the builders to advise their suppliers not to seek to deliver before 7.30am.