In theory yes, in practice no. Both the ANZACs and the Canadians formed separate Corps in 1918. The British were well, the British, the ANZACs and the Canadians were very separate.
Not exactly. Australian and Canadian Corps were very much a part of the British system. They received SS pamphlets just as every other formation did, contributed their learning to the development of further pamphlets, just as every other formation did. And their training establishment, when it wasn’t actually the same organization, followed the exact same rule book.
Where the Canadian and Australian Corps were unique was that they had the political shelter that allowed them to remain as a Corps level unit, when most British Corps were geographic formations that had Divisions rotated through them regularly. This political shelter also allowed the Canadians to maintain a 12 battalion Division when everyone else (including the Australians) had gone to a 9 battalion Division to save manpower. And to basically create a fourth brigade of Engineers for every Division which massively increased their ability to follow up on a successful assault and increase the infantry’s training time at the expense of fewer formations than they would otherwise have had. Again, this was not an innovation the Australian Corps could afford to copy, having a closer organization to the standard British one of the day.
Long story short, In WW1 the Australian and Canadian Corps were very much part of the British army and the two formations learned at about the same rate. The two formations just had some extra benefits that allowed them to be organized differently with some benefits being accrued from that state of affairs.
British only adopted a "doctrine" in the 1970s. They did not have one previously. They refused to develop one previously seeing it as limiting the ability of a commander to respond to a given situation.
British doctrine of the Great War was defined by Field Service regulations. These were very much similar to doctrinal documents produced by other major powers. Though they took care to delegate decision making to the “man on the spot” as much as possible. A concept that later doctrinal statements, particularly in the US, would fall all over themselves to ascribe as unique to German military planning. However, fast was designed to be used by professionals with a considerable time in service. And the Great War included a number of innovations anyway. So things needed to be spread around, reinforced and sometimes dumbed down for those with less time invested in the culture. Thus Sas pamphlets were put out throughout the war.
So yeah, by any reasonable metric, the British army did have a doctrine as we understand the term.