In the context of the First World War, since the film that Paterson Joseph is referring to takes place during that specific conflict, it is very much true that black British soldiers and African soldiers from British colonies were excluded from the 1919 victory parade in London.

I specifically want to highlight historian John Siblon for being the foremost scholar who has examined the debates surrounding the inclusion of African soldiers in the proposed 1919 victory march in London. What is evident is that there were those who did support the presence of black soldiers in the victory march -- for example, former Colonial Secretary Viscount Harcourt urged in the House of Lords in February 1919 that black soldiers from the British West Indies must be included, and that there should at the very least be some representation for East and West African soldiers. Ultimately, however, the decision was taken for the parade to be a more "domestic" affair and actively sought to exclude non-white soldiers from being represented in the victory parade, with the sole exception being soldiers from British India who were not present in that particular victory parade, but were allowed to be part of a separate victory parade just for them. The exclusion of non-white soldiers from the 1919 London Victory March was therefore official British policy, implemented by the planning committee, in accordance with British imperial hierarchy in which black soldiers were considered at the very lowest rung of the ladder (in comparison with soldiers from British India who were seen as belonging to a martial race). Great Britain was not alone in this, either. American General Pershing refused to allow the presence of African American soldiers in the London victory parade. France was the only country who actively did include non-white soldiers in the London parade, defying British policy by including colonial soldiers from North and West Africa as part of the French contingent.

Yet as Siblon points out, and that I would like to emphasize, the exclusion of black British soldiers and African soldiers must be seen in a wider context of 1919. Just as in the United States during the same year, Great Britain saw several instances of collective antiblack violence (or race riots) happening throughout the year. Black British and colonial subjects of the British Empire became easy targets for disgruntled white workers who saw them as competition for work and housing, and who wanted to affirm white supremacy, especially in the light of interracial marriages. This went as far as the National Union of Seamen and other sailor unions trying to bar non-white seafarers from being employed. In the Liverpool race riot, for example, black British ships fireman Charles Wootton was murdered. Many more lost their homes or were grievously assaulted in Barry, Cardiff, Hull, London, South Shields, Salford, Glasgow, and Newport. In addition to this, the British West Indies Regiment in Taranto, Italy, had mutinied in November 1918 after repeated acts of discrimination, including being denied a pay raise while their white colleagues had been granted one. With an already exclusionary view of black British participation in the war (the British West Indies Regiment was not allowed to actually fight against white men on the Western front), this atmosphere of racial hatred certainly contributed to their ultimate exclusion from the 1919 victory parade. As Joseph rightly points out, the presence of black British soldiers (who fought in otherwise all-white regiments on the Western front), African colonial soldiers, and other non-white soldiers was actively excluded from the post-war memory of the First World War in Great Britain and it is only recently that they have begun to be included.

For more, see John Siblon, "Negotiating Hierarchy and Memory: African and Caribbean Troops from Former British Colonies in London's Imperial Spaces" in The London Journal (2016), 41:3, 299-312.

Depicting a Sikh soldier, incorrectly, yes. Imperial troops (i.e non-British) were fielded in regiments comprised of their own peoples (Indian Regiments in the British Indian Army, etc) rather than being integrated into the British Army. Too, most Imperial formations served in theatres other than Western Europe.