M48 Severn Bridge is not surprisingly closed in one direction (East bound), and restricted in the other (West bound). Almost certainly will be fully closed in both direction by end of the day.
Last Monday a high sided lorry was blown into the central reservation and turned on its side, when the tarpaulin was caught in the wind like a sail, and the vehicle went out of control. The driver was thankfully not injured, but must have been very shocked. They won't take any chances now, and will divert high sided vehicles to the Prince of Wales Bridge on the M4.
@OhYouBadBadKitten thanks for the visualisations, they are really helpful. The danger zone for the Severn will be at the top of the estuary towards Newnham-on-Severn (where people ride the Severn Bore tidal flows in the spring). The river is closer to ground level there, so more danger of flooding.