A key indicator of NHS performance is the target to reach 90% of patients within 18 weeks - but there is a backlog of 193,000 people who have waited longer.
A budget of £250m has been allocated to prioritise their care, but this could bring longer waits for others.
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British soldiers will join troops from some 30 countries who work in the country.
The demand comes after the Prime Minister urged a "grown up" relationship between her government and the devolved administrations.
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