I fixed the issue.

The reason for the error was because I was trying to update a file while the file stream was still open. You need to ensure this is closed before updating the physical file.

I achieve this by the following:-

To close a stream either explicitly call .Close() method on the stream object OR use a "using" statement. I did the latter:-

using (var stream = _mediaFileManager.GetFile(mediaItem, out string mediaPath))

Inside this using statement, use Image.Load(stream) and store the Image object globally so you can use it outside of the using statement. Then, outside of the using statement, create a new memory stream:-

using (var newFileStream = new MemoryStream())

and use your image object and call one of the SaveAs methods (depending on the extension) and load this into newFileStream. Then call the code above using your new memory stream:-

item.SetValue(_mediaFileManager, _mediaUrlGeneratorCollection, _shortStringHelper, _contentTypeBaseServiceProvider, Conventions.Media.File, item.Name + extension, newFileStream);
mediaService.Save(item);