Motorways were built by the Road Construction Units, staffed by a mix of local and Westminster government employees but run by the Ministry of Transport who set standards and controlled the money.
The Motorway Network was designed and funded by the Ministry of Transport, but delivered locally, as was the case for many non-M strategic roads - which is why you get oddities like the A50 being tarmac in one county and concrete in another.
Britain's first stretch of motorway - the Preston Bypass (now part of the M6) - was built by Lancashire County Council, back in the days when we had big powerful councils with meaningful in-house surveying and public works departments. It set the template for the Special Roads Act.
The first 26miles of the M5 were build with Worcestershire County Council acting as engineer, in many cases doing a better job than government - for instance the CC, Police and County Surveyor had to make repeated representations to the MoT that it ought to be 3 lanes (the government wanted to cut corners and build a dual carriageway - some things never change!). Southerly sections where built with Gloucestershire and Devon County Councils acting as engineer.
So yes, it was collaborative - but Westminster laid out a strategic map and provided the money for the Councils to get on and commission the actual work. Something that would be very difficult today.
This was also basically how the US Interstate Highway network got done - the USGov drew up a strategic map, with construction delivered by states.
Personally I've never seen a local authority that could consistently find its own arse with both hands, they tend to be composed of retired or unemployed middle managers who can't bear not being in charge of something, together with some idealistic younger folks who think they can change the world but have no understanding of economic reality.
And yet, your bins get emptied, the schools are open and a road network exists (even if the potholes are a pain because Westminster witholds the cash to fix them, and denies them the revenue powers to do it themselves). No organisation - public or private - is perfect. It's only that local authorities who have to live with that cursed triad of statutory duties, funding coming on the whim of Westminster and limited revenue powers to make up the difference. Central government has all the power (even if they choose not to exercise it...), and private businesses can go looking for alternate revenue streams, or drop products/services that aren't paying their way. Councils don't have that luxury with statutory duties.