Definitely not codswallop.
Wetherspoon have not made an official announcement yet and so their customer care people have no knowledge of what is happening ...a similar thing happened when The Ship of Fools at West Croydon closed. The Capitol staff were told over the weekend but were asked to keep it quiet and, of course, they didn't and will not publicly acknowledge that
So Wetherspoons have definitely sold the lease and are closing the pub. The staff believe that it will become a cinema but that is not so certain as there are several things to be done. It is a listed building so can't be used for property development. Planning permission/change of use also need to be finalised but a cinema should be a formality.
However, as with any property change, things may still go wrong.
It was definitely a cinema in the past, 60 years ago my girl-friend remembered going there at the age of 9, buying a ticket and then opening a back-door ticket to admit all of her friends.
Fron the Wetherspoon website :-

The Capitol opened its doors to the cinema-going public in 1929. Later renamed and converted into a bingo hall, the building now bears its original name.
A rare survival of a 1920s cinema, The Capitol, on London Road, first opened its doors to the cinema-going public in 1929, with a screening of Man, Woman and Sin. Renamed the ABC in 1968, the cinema gave its last picture show in October 1973. There were plans to convert and even demolish the building. However, The Capitol opened as a bingo hall in February 1978, closing in the first week of December 1996. It is now this Wetherspoon pub.

Definitely not wishful thinking on my part. As an OAP with limited funds I love Wetherspoon pubs as I can't afford to pay £4 plus for a pint for those ghastly gastropubs in Lordship Lane and Forest Hill. So I would much prefer the status quo.

Oh well, I still have the Fox on the hill, Brockley Barge and The Moon and Stars in Penge, but none of those of those is as convenient as The Capitol.

No knowledge of who the new lease holder is, the staff were told it would be a 3 screen cinema but that could be difficult without considerable changes to a listed building.