I too have come upon that statement in Higman's paper and wondered which manuscript he is referring to. There are two "papers" of Erdős and Rado that I think it might be.

First, it could be a reference to what became their [solution to problem 4358][2] in the <i>Monthly</i> in 1952.

Second, it could instead be their 1959 paper "[A theorem on partial well-ordering of sets of vectors][1]" (<i>J. London Math. Soc.</i> (1959), 222–224).



  [1]: http://jlms.oxfordjournals.org/cgi/reprint/s1-34/2/222
[2]: https://doi.org/10.2307/2306526