At the university where I work, each course has a separate pool for British students and international applicants.
So there are x number of places for British students and the British applicants compete for those places. And there are y number of places for International students and the International applicants compete amongst themselves for those places. There is no direct competition between a British student and an International student in that sense.
The setting of numbers for the British and International pools for each course is a somewhat complicated process, taking into account demand, quality of applicants / students, income generation and what this income might be spent on at course level (e.g., the income from International students might be earmarked to pay for more staff) and at university level (e.g., medium and long-term plans to build more accommodation and other facilities), how many International students other courses want and how this relates to the physical capacity of the university and its aspirations as a university in the world.
International students are inevitably a heterogeneous group. Some will want to mix with British students, some will prefer to seek out others from their own country. All universities with a lot of International students will acknowledge that there can be issues with International students splitting off into their own single nationality / linguistic groups and, while acknowleding that this may be their preference and may have some emotional and sometimes practical benefits, see this as an undesirable outcome for the students themselves, other students and the university as a whole. It is a difficult balancing act.
Courses with a lot of International students usually do a lot of behind-the-scenes work to promote some degree of mixing between British and International students in an academic setting (which is all they can control). As an example, we set seminar groups and small groups up carefully to balance the numbers of British and International students, rather than just letting people choose or doing it alphabetically which we have seen leads to the creation of almost exclusively single nationality groups due to where their names fall in the English alphabet.