The British organized JEF (Joint Expeditionary Force) has accepted its first two non-NATO members: Sweden and Finland. Originally formed in 2014 with contingents from Britain, Denmark, Estonia, Latvia, Lithuania, Netherlands and Norway the JEF has not yet become operational. That is not expected to happen until 2018. JEF contributions are limited to commando and other infantry units trained and equipped to move into action quickly. JEF also accepts air force and naval elements of a similar nature. This is why Britain is the lead member because Britain has the most long range military air and naval transport capability.
JEF is meant to supply, on short notice, a small force (of a few hundred troops) that can be sent anywhere in the world to deal with a crisis situation that would benefit from immediate attention before it turns into something larger and more difficult to deal with. Closer to home, JEF could put a force of up to 10,000 troops (land, air and naval) into action quickly. This option appears aimed at Russian plans for surprise attacks like those used successfully against Ukraine in 2014 (successfully to seize Crimea) and less successfully in 2015 (to take the Donbas area of east Ukraine).
After the Cold War ended in 1991, NATO nations began planning rapid reaction forces based largely on using conventional forces for emergencies within or adjacent to NATO member nations. This concept was expanded with the formation of the EU (European Union) in 1993. That was because at the same time the EU was formed there was a major crisis next door in the former communist state of Yugoslavia, where a civil war had broken out. The EU was meant to be an economic/political union. The EU has purely European and had more European nations as members than NATO did. Despite the existence of NATO, plans were soon underway to establish some EU military cooperation as well.
By 2000, fresh from the peacekeeping crises in the Balkans, the EU succeeded in gathering a considerable number of assets for its new Rapid Reaction Force. However, it found that post-Cold War European nations lacked much in the way of support forces. That was because most of what they had was already pledged to NATO. So the new EU force came mainly from larger nations. The contributors included Britain (an armored brigade, a marine brigade, 72 warplanes, an aircraft carrier, two SSNs, four surface warships and five support and amphibious ships), France (12,000 troops including tank and engineer brigades, 75 warplanes, 12 warships including an aircraft carrier), Germany (13,500 troops), Italy (6,000), Spain (6,000), Netherlands (5,000) and smaller contributions (totaling 12,000) from Greece, Austria, Finland, Sweden, Belgium, Ireland, Portugal and Luxembourg. Denmark was the only EU member to refuse to contribute but Turkey, seeking to join the EU and long a member of NATO offered a mechanized brigade and 30 warplanes.
This EU force quickly evolved into EU Battlegroups, a system in which the Rapid Reaction Force members arranged to take turns contributing two or three “battlegroups” (a reinforced combat battalion) to be available for six months for quick deployment. This went into effect in 2005 and is still operational. After 2014 the focus turned towards potential emergencies involving the new Russian threat. That encouraged Germany to offer an integration option, which several East European nations expressed an interest in.
In 2012 Britain pointed out that the most frequent type of emergency European nations face are often smaller ones occurring far from Europe. This led to the JEF, which may indeed get into action long before the existing, and larger, European rapid reaction forces.