NHS & Additional Health Insurance

Dear Colleagues, I will come to London with a MSC Fellowship this autumn, together with my partner. As far as we've understood, there should be no problem for either of us to get accepted by the NHS – or did you encounter any difficulties with that? And, based on your experiences, do you consider NHS coverage sufficient, or would you rather recommend choosing an additional private insurance, either from the UK or from one's home country, for the time in the UK? Any advice is most welcome, many thanks in advance! Christian