The Independent (UK) carries an interesting story about Michael Lyons, a member of the British Navy who has apparently applied for status as a conscientious objector:

Lyons became disillusioned with the Afghanistan war after attending a training session where he was told that saving military lives would take priority over those of civilians. His view strengthened after revelations about high losses of civilian lives reported on the whistle-blowing website WikiLeaks.

The article seems to imply the UK military hasn’t seen as many CO applications as the US military has: 

When his application was heard last December, Lyons was the first person to appear before the Advisory Committee on Conscientious Objectors (ACCO) since 1996.

However, the ACCO only hears appeals for CO applicants who have had their request denied.  Other documents indicate there have been six successful discharges as COs since 2001.  Still, it appears the concept of conscientious objection is more nebulous in the UK than it is in the US.

In the end, the committee said his opposition was “political rather than moral,” so it denied his claim.  Those who are advocating for his cause seem to think that’s actually a good enough reason, referencing the vagueness in the definition.  They appear to be advocating for CO to be explained to new recruits, and perhaps for the law to be changed to include other objections besides moral or religious ones.

Since his CO application has been denied, he reportedly may face charges for his refusal to train for the war.