It really depends on the specific funding. Some funding sources are for UK/EU citizens only. Some are for legal UK residents (though some stipulate that you must have ILR or have accumulated a minimum UK residency time first, typically 3 years). Some are for anyone who qualifies for the degree course and it's up to the discretion of the institution to award funding according to it's own eligibility criteria (e.g. financial need). Some degrees are fully or partly funded or sponsored by a corporate partnership, and they may have different eligibility requirements than if the funding came from the university. Some charities will partly or fully fund PhD courses if the subject is something related (e.g. Cancer Research UK).
I'm unable to do a PhD at the moment due to health issues, but when I was pursuing one a few years ago, funding opportunities were varied with equally varied rules of eligibility depending on where the money came from (the institution itself, a grant specific to the department/supervisor, company partnership, professional organisations, and so on). Your best bet is to contact the institution to work out what opportunities are available, and potentially, your supervisor may know of a few specific sources as well. Depending on the field you're doing the degree in, are there associated professional bodies that offer funding opportunities? (e.g. for a biomedical-related degree, potentially look into the Royal Colleges, Royal Societies, and regulatory bodies like the IBMS or ACS)
Personally, if funds weren't available and I would be paying for the whole thing myself, I would wait until being classed as a home student as those fees are substantially less than being an international student. If you can find a scholarship option that's available to you now though, go for it!
Whatever you decide, best of luck!