In lab science, it would be nigh on impossible to self fund a PhD via one's own saving etc. As well as your living expenses (variable) and the university tuition fees (~£5000/year) you would need a huge amount of money for lab costs/equipment/consumables: ~£10-20K per year.
I suspect when labs say they are willing to take self funded students, they mean that they are happy to have someone do the work, so long as they bring their own studentship/fellowship funding with them e.g. international students who have sponsorship from their home governments, or UK students who take the project proposal and make an application to Wellcome/the MRC/BBRSC etc.
If you are interested in a particular lab, get in contact with them and have a chat about what the state of play is. It may be that they are planning to apply for a project/programme grant in 18 months time, and if they think you would be a good candidate to join them they will write your project into the application. In the meantime, you might get some research assistant work, which would be great experience for you.