After London

The heads of state of the six Western industrial nations and Japan that attended the London economic summit now have their work cut out for them: translating the broader goals of the conference into specific legislative and governmental actions that will ensure continuing global economic growth.

That requires bolder action than has been the case to date - and indeed, firmer action than the generalized statements of common purpose voiced in the conference communique. For the United States in particular - which was criticized by some participants for its huge federal budget deficits and high interest rates - it is imperative that a comprehensive policy be enacted to deal with the deficits.

At the same time, economic factors were to a large extent overshadowed by international concerns - especially East-West relations. Compared to the tone of last year's meeting at Williamsburg, Va., this year's discussion was far more conciliatory, calling for the ''speedy resumption'' of arms talks. With US-Soviet relations at a particularly low ebb, it is imperative that arms negotiations resume as quickly as possible.

Still, the economic statement gently - although indirectly, without naming the United States - suggested the US should reduce budget deficits. What was somewhat left unsaid, of course, is that all the industrial nations need to take specific actions:

European nations need to avoid an increasing drift toward trade protectionism. Japan needs to open up its large domestic market to exports - even while restraining somewhat its ambitious scramble for market dominance in both Europe and North America.

The conference itself, for all its shortcomings in failing to produce a united approach toward such issues as interest rates and trade protection, was clearly useful. The government leaders, of course, welcome the media attention that invariably accompanies gatherings such as these. That is not unexpected. But on a deeper level, such a conference - and this was the 10th annual economic summit of the industrial nations - once again presented the leaders an opportunity to meet together, pinpoint differences, and discuss concerns. Private discussions about such issues as terrorism (which the conferees condemn) , the possibility of a shutoff of oil supplies through the Persian Gulf, and East-West arms negotiations, were often more important than the public meetings. Of course, much of the conference's formal statements, such as the rejection of the use of force to settle disputes, are important guidelines for the future. And summit leaders pledged to assist debtor nations.

Indeed, the London conference once again underscores the importance of face-to-face communication among world leaders. That is why such an institutionalized, regular get-together between US and Soviet leaders would be a welcome development. Mr. Reagan has yet to have a private meeting with the head of the Soviet Union. Regular US-Soviet summit conferences by themselves would not remove all the major differences between the two superpowers. But it seems far better for the two sides to be talking out their differences than to resolve them through a tit-for-tat arms race that, at this juncture at least, shows no end in sight.