Ms.Tahira, if you do the medical examination in UK, please go to a large public hospital. In fact, an experienced friend told me that there is no need to get the Medical Examination in applicants' own country because the medical examination should also be done at the Entry-Exit Inspection and Quarantine Bureau when they apply for Residence Permit in China. Z visa holders have to apply for residence permit within 30 days after entry.

We are currently in Laos, and will be traveling to China to take up Teaching positions but require a medical certificate for our visa application.
Our school has requested this also.
Which hospital or medical surgery in Vientiane can we obtain this?

the medical certificate should be done from the hospital, which gets permit of the Consulate in Vientiane