Also self-employed people, who wish to work in Germany, can choose the AOK. That applies to self-employed people from the EU, EEA countries and Switzerland. But also foreign nationals from countries outside the EU, who are allowed to work in Germany according to their residence permit, have this right to choose the health insurance company.
As in the British health system, you are not obliged to wait until you are covered by your statutory health insurance fund. You are entitled to use the services already from the first day of membership. As a self-employed person, using the AOK services is convenient with the AOK health card. Like in Britain, you are not expected to pay costs up front. And the contribution is neither geared to your state of health or your age, but rather simply to your income. You can find information on the contribution rates here.
A further advantage: Family members (spouse or children) without an own income source can be co-insured without paying any premium. The contribution rate remains the same for the member, no matter how many family members are co-insured.