Funding has many variables--what is available through a department, whether you and your institution are eligible for ESRC or other types of funding like that, whether industry pays your funding, whether, if you are not from the UK or EU, you are eligible for funds, and whether your own home country has funds available.
In the US, people generally take out student loans if needed--widely available--to fund education, including PhDs, and maybe work on the side, or do Graduate Teaching, or whatever, to supplement the loans. Fully funded post graduates would be few and far between. I never thought twice about the funded/self-funded issue because from my American lens, self-funding is pretty normal.