It certainly won't be a ghost town.
Cabo Roig is a popular place for golfers to stay, with many courses within easy access. January and February are popular with golfers and their families from the UK, but the place will be nowhere as busy as other months.
Most of the bars and restaurants will be open, with only a few closed for refurbishment or for the owners annual holidays, which is normal in all parts of the Costas.
There is a large retired population and other people like you, wanting to escape the worst of the UK weather. There are plenty of activities to keep them busy.
There is a bus service, and I know that coach trips are often organized with local pick-up's to places of interest, at very little cost. Again, the local English newspapers are the place to find out exactly what is happening, or just get chatting with other people.
If you are looking at apartments, then it might be a good idea to enquire if there is any form of heating. It doesn't have to be full central heating, of course. That would be very unusual! Just something to take the occasional nip out of the air.
I can see no reason why you wouldn't have an enjoyable few months.
P.S.
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