I walked the Inglés this January, and had no issues with finding an open albergue along the way! The entire Inglés is in Galicia, and the Xunta makes a point of having the municipal albergues open all year round.
In Pontedeume, the municipal albergue is excellently located on the bank of the river, but it's unmercifully cold as the building is an old one, thin-walled, and not equipped with any kind of heating (the showers do have hot water, though), so I'd recommend finding private accommodation - thankfully, the town has lots of them.
The albergue in Betanzos is a true five-star Xunta albergue, and the one in Hospital de Bruma is also good - it's well-heated, except for the bathrooms which are located in a separate small building without heating.
In SigĂĽeiro, there's no municipal albergue and most of the private ones close for winter, but the town also has a number of hotels - I had no trouble finding a nice room.