Churchill had quite a few options when it came to what uniforms he was entitled to wear.
His first regiment was the 4th Hussars. On the North-West Frontier, however, he was attached to the 31st Punjab Infantry and in the Sudan to the 21st Lancers. In South Africa there were the Lancashire Hussars, and, after his escape from captivity, the South African Light Horse. In pre-1914 years he was in the Queen’s Own Oxfordshire Hussars (a yeomanry regiment), rising to the rank of Major and regularly attending, even when a senior minister, their summer camps. In France after his resignation from the Government in November 1915 he was attached to the 2nd Grenadier Guards before commanding a battalion of the Royal Scots Fusiliers. In the Second World War he frequently chose to wear the uniform of an RAF air commodore and he appeared at Yalta as a colonel of Hussars. For naval occasions he usually wore the outfit of an Elder Brother of Trinity House.
I’m pretty sure that he was never a member of the RYS, so the uniform above is almost certainly that of Trinity House. In those days, too, ministers had their court uniforms and Privy Councillors theirs (complete with sword!). He would also have had a uniform as the First Lord of the Admiralty, although whether he could continue wearing it after leaving that office I don’t know.