The 10-year-old girl recently completed a five-day course of chemotherapy at the London Clinic without problems, but was prevented from leaving after developing an infection.
The girl, who last month lost a legal battle against Cambridge Health Authority to continue chemotherapy, remains on antibiotic treatment but is well enough to go outside in the spring sunshine.
Dr Peter Gravett, the haematologist who is treating the girl at the private clinic, said: "She now feels well and has been enjoying the playroom and visiting the park in the fine weather.
"During the next few days we will be testing her bone marrow to assess her response to the chemotherapy and this will determine what further treatment is given, if any."
Child B's case became news when her health authority refused funding for further treatment on the grounds that it would be too distressing and unlikely to work.
The High Court ruled against their decision but this judgment was later overturned by the Court of Appeal.
Her course of chemotherapy, which cost £15,000, was eventually paid for after an anonymous donation of £75,000.
Dr Gravett will announce a further update tomorrow.