BTW I've got TRVs, can i rely on them to close and stay closed?

Not usually. However, there are 3 solutions.

1. Some TRVs have a genuine off position that isn't the frost guard setting.
2. Most TRVs allow you to install a "decorators" cap instead of the TRV
head.
3. Most TRVs allow you to put a suitably terminated stop end on the valve
outlet, so it doesn't matter if they open.

Christian.