long odds to get admitted to PhD programme with 2.2. It is already competitive with first and 2.1. Theoretically, it can be done if you can find a supervisor. I know a young woman in STEM who got only a 2.2 and was admitted without funding straight from undergrad. She was self funded/had supportive parents. Her cousin was in the same subject, same year and got a first. The cousin got tuition waiver and a nice stipend with preferential research/publication projects.