Note that the Liberal Party would be very likely to remain one of the main party of the government (i.e. free trade). Besides, empirical evidence found that Imperial Preference actually had a negative impact on British industrial productivity over the long run.
The US would be isolationist for much longer ITTL. During near term Germany would be the only competitor.
While no expert in UK politics it is not simple enough to assume the Liberal Party will remain ascendant or that free trade will be a viable policy longer term, especially if we see a major shock such as the Depression, itself not entirely butterflied so easily here. Perhaps I should have used quotes but I can foresee even "Free Trade" sold as a trade agreement binding the Commonwealth and setting barriers to outsiders. We need to know more on how the domestic economy evolves as well as the political environment. But if as you opine that free trade holds longer then it benefits the German recovery from the war (assuming that still occurs here) and likely hastens the industrial decline of Great Britain with an accelerated emergence of the "post-industrial" service economy in the UK.
My opinion is that the American oil majors are as aggressive as ever and have plenty of power to get ahold of oil reserves in the Middle East without American government intervention, in fact the government will likely be pushed to pursue a de-colonial agenda which will worsen the relationship between the USA and the UK. If you are correct on free trade this will not get overly frosty but if the Commonwealth pulls tighter together to exclude American exports than we see the USA and UK getting chilly in their relations, and I surmise this can fuel warmer relations with Germany, especially if they too need open markets, thus my premise for a long term "Special Relationship" between the USA and Germany founded on trade and antagonism towards the colonial powers. Strange new paths open as butterflies tend to flock after the money and power.