RAF transport was generally by road, as few airfields were near rail. Army main Base Ordnance Depots e.g. Bicester had extensive railhead sidings so could use rail more easily.
From my wartime childhood I remember the Queen Marys - the 60 ft long Bedford artics that hauled aircraft in sections all over the country (there were some Crossleys but principally they were Bedford Series O). I remember many country lanes with signs saying 'Unsuitable for Queen Marys'. You bet! Google Bedford Queen Mary for lots of photos.
RAF also used a lot of AEC Matadors for all manner of uses - general transport, Coles mobile cranes and bowsers.
As there was no private road traffic and only local civilian delivery lorries and buses the road network was almost entirely for military use. Don't think you have to have motorways for extensive road transport.
By the end of WWll 1 in every 9 British soldiers was in the Royal Army Service Corps - the Army's Supply and Transport Corps.
And nobody thought much of long hauls that would surprise you today. For instance in 1946 my mother, young brother and I lived with my father in the tented RASC transport base he commanded in the desert near Mafraq Jordan (where the refugee camps are now). He had over a thousand soldiers with several hundred 3 - tonners (mostly Dodges with some Bedford Os) whose job was to haul over 100,000 Italian and German POWs from their prison camps in Iran and Iraq to Haifa for shipment home. It took a year. Think of those 3 tonner convoys (20 POWs per truck) at 20 miles in the hour on that trans desert long haul.

The book 'Croissants at Croydon' by Jack Bamford goes into considerable detail about the movement of aircraft spare parts and fuel. A thumping good read for anyone interested in aviation.