Hi - so on what grounds if any would you appeal?
The key photo we need to see is what is the signage now here, (where you turned left into Custom House Street)
https://maps.app.goo.gl/MysPKh7ZnS4XufBS6This is the latest view (October 2020)
If you follow this sign on the Callaghan Square roundabout for the Marriott Hotel: -
https://maps.app.goo.gl/8CMtkvtDscaZZUqx6It brings you to here, the entry to St Mary Street
https://maps.app.goo.gl/cDEzinWGnnFWTmLw6Then at the top, having passed under the railway bridge, you then come to a set of traffic lights that allow you to turn right into Mill St.
https://maps.app.goo.gl/F7dnhNEqxfkh987f9the sign is shown as far back as 2012 in GSV.
Custom House St has been buses only from that sign for some years, but in the other direction, one could go along it for access. However, this means "access to premises on Custom House St, not to gain access to the next junction.
Both this forum and the now-defunct Pepipoo have seen what chaos Cardiff council have created, and one has to wonder if it's just a cash-generation exercise. I would certainly complain to the Marriot management about the totally inadequate instructions on how to access their hotel.
There is no other approach one can take to get to the Marriott. If coming from the west along Penarth Road and turn left to keep on it, you cannot go under the railway bridges, to get to St Mary Street as No Entry signs bar your way
https://maps.app.goo.gl/RQp3uNGcreR15ANb9The bottom line, is that there is only ONE possible approach to Mill St and the Marriott. How Cardiff council think strangers to their city can possible work out how to get to their hotel, I don't know.But of course they are also in the "DGD Club", (DGD ? - Don't Give a Damn)