This was easier said than done because Britain already had large numbers of men in an army committed worldwide: in Germany (BAOR), the Middle (MELF) and Far (FARELF) East. The bulk of these comprised National Service men. The consequence was increasing the length of NS from eighteen months to two years and the liability to serve in Korea. Up to two thirds of any army unit in Korea were NS men.
The first response was to rapidly put together a force from those in Hong Kong; this known as 28th Brigade (basically just two infantry battalions the Argyll and Sutherland Highlanders and the Middlesex Regiment) reached Korea in late August 1950, where in very desperate circumstances it was immediately in action. Meantime 29th Brigade back in the UK had to be assembled, trained and equipped and sailed with supporting tanks and artillery in October 1950.