British "Meddling in Europe"? The British might call it strategy for survival.
The term / policy is called Britain's "Balancer Role". It's a long standing strategy where Britain opposed the strongest nation on the continent not based upon value, interest, culture, or threat. But based upon the long term strategy of maintaining a balance of power.
Within the European balance of power, Great Britain played the role of the “balancer,” or “holder of the balance.” It was not permanently identified with the policies of any European nation, and it would throw its weight at one time on one side, at another time on another side, guided largely by one consideration—the maintenance of the balance itself.
This is where the term balance of power comes from, or at least is a very famous example of it. Britain's policy, was not to "curb the growth of all-European empire". It's basis was with Britain's strong Navy, and Island geography; no country would be in a position to invade them if a balance of power were maintained on the continent. This policy was said to be the motivation for Anglo-Spanish War, the Napoleonic wars, WWI, and Churchill mentions it in "Gathering Storm" as why WWII occurred. Namely the Allies failure to maintain the balance of power due to:
- Neville Chamberlain policy of appeasement,
- France's failed obligation in defense of smaller nations
- The United State's policy of neutrality
Discussion, Explanation of Gathering Storm
“in keeping with a 400 year history to avert a dominance by a dictator from any country We ought to set the life and endurance of the British Empire and the greatness of the this island very high in our duty, and not be led astray by illusions about an ideal world, which only means that other and worse controls will step into our place, and that future direction will belong to them.
Your Question: Was there a "European Balance of Power
Strategy" for Anglo-American interests in between 1925 and 1935?
At first thought I would say absolutely not. America barely had an Army in the interwar period, certainly not sufficient to make the US a concern in a European balance of power.
US Army was smaller than Portugal's when WWII began in July of 1939.
As Churchill eluded too in "The Gathering Storm" he believed the nearly 150 year old American policy of isolationism and neutrality was a major failing of the allies which lead too WWII; 1 of 3 major failures by the allies given above.
Having said that however their was the "The Washington Naval Conference, 1921–1922", and the Five-Power Treaty which came out of it.
The Five-Power Treaty
The Five-Power Treaty, signed by the United States, the United Kingdom, Japan, France and Italy was the cornerstone of the naval disarmament program. It called for each of the countries involved to maintain a set ratio of warship tonnage which allowed the United States and the United Kingdom 500,000 tons, Japan 300,000 tons, and France and Italy each 175,000 tons. Japan preferred that tonnage be allotted at a 10:10:7 ratio, while the U.S. Navy preferred a 10:10:5 ratio. The conference ultimately adopted the 5:5:3 ratio limits.
The US and Britain received the largest allotments of capital ships (battle ships) in this treaty it is said because they both maintained Atlantic and Pacific two ocean navy's. I would say the fact that Britain and American negotiators were willing to accept parity with each other, could be and probably was an indication that both nations saw a likelihood of a conflict between each other as remote. Perhaps evidence they were at a bare minimum thinking of working together?
Still it's pretty weak evidence. The US returned to it's neutrality / isolationist roots in the inter-war period between WWI and WWII. The United States did not build a fleet which had parity with the British Navy after WWI, even though by treaty they could have. Finally the United States did not come to Britain's aid militarily for years after she faced existential threat from Germany first starting in 1939. When the United States did enter WWII, it did so only after the US was attacked, and Germany declared war on the United States first (Dec 1941).
So my answer is:
Perhaps: Perhaps in 1920's it was a thought by planners of both nations to pursue some sort understanding / arrangement which would work for both the Empire and the US interests/security. Such an arrangement would certainly seem to have made sense in the 1920's with what we know today. That thought ultimately was not followed up on; however, probable due to a lack of (short sighted) political interest. Lack of interest certainly the United States, who couldn't even get support in the domestic legislature to join the league of nations, and organization which the United States President Wilson has championed, lobbied for, and helped organize. Politically the US was very motivated to get back to it's isolationist roots in the decades, prior to WWII.