Yes, quite a few actually.

Probably most notably was one Winston Spencer Churchill who was demoted/resigned from government following the Dardanelles debacle and subsequently commanded a battalion of the Royal Scots Fusiliers while still remaining a serving Member of Parliament.

Another example is Charles Duncombe, who was a serving Member of Parliament, representing Thirsk and Malton. He was also an Officer in the Yorkshire Hussars. Though he ceased being an MP when he inherited his father's title in 1915. He was killed in action at Flers in 1916.

In fact, some 19 British MP's were killed in the first world war, not including those from the House of Lords.

Meanwhile Asquith, Britain’s Prime Minister at the start of the war, lost a son, while the country’s future leader Andrew Bonar Law lost two sons.

Apart from Churchill, several other future PM's fought including Eden, Attlee, and Macmillan - Eden losing two brothers killed and another seriously wounded.

In the second war, a further 23 MP's were to lose their lives in uniform.

They have but, at least with respect to World Wars One and Two, it has required special legislation to make it possible. For instance in World War One a bill was passed "House of Commons (Commissions in His Majesty’s Forces) Act 1914" which allowed current members of the house to continue being members while also joining the Armed Forces. There are more details here : https://commonslibraryblog.com/2014/08/04/1290/ (under the heading 'The War and MPs') . By January 1915 there were 184 members in the military out of a total of 690.

As things stand today it's not legal for members of the British armed forces to stand for elected office (http://webcache.googleusercontent.com/search?q=cache:Ku5SVYBFJTEJ:www.parliament.uk/documents/joint-committees/human-rights/Briefing_from_Forces_Watch_Terms_of_service.pdf+&cd=7&hl=en&ct=clnk&gl=nz).

It's not much of a source but I remember reading in a biography of the mountaineer Chris Bonnington that while an Army officer, in the 1960's, and wishing to leave the army he was able to stand as an MP in a by-election and this meant he had to resign his commission immediately (regardless of the outcome of the by-election), something he wanted to do but was otherwise restricted from doing. So this suggests that certainly in the 1960's being an MP and an Army Officer simultaneously was not possible. That story comes from "I Chose to Climb" by Chris Bonnington.