Forgive me for jumping in here and I hope I'm not muddying the pool, but my understanding is that there is some difference between the two visas. If you get your visa in London (O-A visa), you must have or obtain health insurance to cover you in Thailand. If you get your visa here (O visa), you don't have to have insurance.
As long as your home country insurance will cover you in Thailand. This can be tricky. Some insurance does, some doesn't and some only provides limited (e.g. 60 days) coverage.