Like I said, I think the primary reason is that US MFE programmes are generally under business school or taught jointly by several department (so students with weak math background can choose units that are not too math demanding) while Oxford MCF and
Imperial MF are entirely taught by the math department and their course content is designed for math students.
The second reason might be due to the different undergrad system between UK and US (or more broadly speaking Europe and North America ). US undergrad students have incredible flexibility to choose units across different faculties and could have several majors. Majoring finance/econ/CS does not mean they did not have studied advanced mathematical content. I have seen some US/Canadian students majoring econ got offer from the two UK programmes and their unit choice include all essential math components for quant (analysis, probability, statistics, differential equations, ML...). But for UK students, it seems that i have only seen math/stats/physics (or joint degrees like math and cs or math and econ) students being admitted.
You could find below description from
Imperial MF course specification: Degrees in Accounting, Economics, Finance, Business or Management with very little Mathematics content will not meet our entry requirements.
https://www.imperial.ac.uk/media/im.../G1U4-MSc-Mathematics-and-Finance-2023-24.pdf; and for Oxford: Applicants should have a background in probability, statistics, ordinary and partial differential equations, linear algebra and analysis. They must demonstrate their aptitude for, and knowledge of, mathematics, particularly in the area of real analysis.
MSc in Mathematical and Computational Finance | University of Oxford.