Good question!

There are a few facts about the British Parliament that account for some of these “holdouts”.

First, the Speaker of the House of Commons (in this case a very interesting chap named Edward FitzRoy) is not a member of the government and so does not count as a member of the government.

Second, Irish Nationalist MPs do not take up their seats as they refuse to swear allegiance to the monarch (in this case George VI). There were two Irish Nationalist MPs in the wartime parliament.

Third, there are also some independents and small parties who did not technically join the coalition: Willie Gallacher was elected for the British Communist Party (the last Communist elected in the UK) and did not support the government and two others who I do not really know anything about to speak on with any level of knowledge were elected as independents.

The next thing to be aware of is that most of the MPs in Parliament in 1940 were already members of the government. The 1935 election had seen a continuation of the National Government formed in 1931 which included elements of the Labour and Liberal Parties but was heavily dominated by the Conservatives – this grouping took 429 of the available seats (although as mentioned above we must subtract one from this figure as FitzRoy was a Conservative MP prior to becoming Speaker).

The Labour and Liberal MPs joined the government when their respective leaders – Attlee and Samuel – joined Churchill’s coalition. Labour brought in 154 MPs and the Liberals 21. Thus we reach your Wikipedia total of 604 (it is of course actually 603 but I assume the Wikipedia editor simply forgot to remove FitzRoy). Question answered!

But wait! Things are not actually that simple. While technically there were 603 “members of the government” because there were 603 MPs whose parties were part of the coalition, this does not actually mean that the government could ever count on 603 votes. In reality there were quite a large number of Labour MPs who did not consider themselves to be part of the government and instead continued to view themselves as de facto members of the opposition. Most prominent of these was Nye Bevan. He was joined by his allies in the socialist wing of the Labour Party including Andrew MacLaren and Ness Edwards. Frederick Cocks, another Labour MP (probably most famously known for being on the Nazi Blacklist and for having the unfortunate middle name Seymour) was also a dissenter.

To go into detail of the actions of these figures is somewhat outside the scope of your question and so I shall be very brief. They frequently butted heads with the government, most often on the issue of press censorship – Bevan was the editor of Tribune, a socialist weekly. Bevan’s biographer, John Campbell, famously referred to him and his allies as “maverick malcontents” during the war. Bevan was an excellent parliamentary orator and frequently outshone Churchill. During the dark days of the war in 1942 when Britain was reeling from a series of defeats, Bevan produced an oft-quoted dig at Churchill, suggesting he “wins debate after debate and loses battle after battle”. There was also criticism of the poor wages given to miners, the conditions in factories, profiteering from business owners and the elitism of the armed forces.

Whenever I am discussing this period of history, I always take advantage of it to highly recommend AJP Taylor’s English History 1914-1945, which to me remains the greatest work of historical writing produced in the 20th century. Arthur Marwick’s many books on this period are also worth reading, although they are in my humble opinion, not as engaging. The best recent work on the coalition government is by Roger Hermiston, it is called All Behind you Winston. He does not shy away from criticism, but he also lacks the clear agenda that limits many historians of this period.

If you have any other questions, I shall do my best to answer them.