Appealing to the Supreme Court is likely to an extremely rare event for most practitioners. The Supreme Court has its own specific rules.
“The Supreme Court has its own Directions which replace the Civil, Criminal and Taxation Practice directions and standing orders of the Appellate Committee Practice of the House of Lords.”
There are revised Practice Directions dealing with appeals which came into force on the 1st November 2013.
Details of the revisions can be found at http://www.supremecourt.gov.uk/news/revised-practice-directions-november-2013.html
All the relevant Practice Directions can be found at http://www.supremecourt.gov.uk/procedures/practice-directions.html
For guides and links to appealing to the Court of Appeal see https://civillitigationbrief.wordpress.com/2013/08/02/guides-and-links-to-appealing-to-the-court-of-appeal/