From American Heritage:

1. Of high cost or worth; valuable. 2. Highly esteemed; cherished. 3. Dear; beloved. 4. Affectedly dainty or overrefined: precious mannerisms. 5. Informal Thoroughgoing; unmitigated: a precious mess.

Precious = dear

That's how I meant it. It sounds dear to my ear to hear a Britisher say that someone has gone "to hospital." Just plain dear, my dear.