You start at L7. Promotion to L6 then requires you to referee at least 20 games and you will be observed on some of these. Similar applies to 6-5. It is also possible to go from 7-5 in the same season, essentially this divides the promotion season into two periods of 1st March to 30th September and 1st October and 28th / 29th February, and the 20 game requirement exists in both of these. All promotions up to and including L5 are dealt with by county FAs.
For promotion from 5 to 4 the CFA carry out the observations but the FA set the criteria and ultimate make the decision. For a candidate to be nominated they must have averaged at least 73 in technical observations over at least 5 games. If they have only had 3 or 4 observations they must also be in the top 50% of the club mark merit table on their main league(s). They must have refereed at least 20 games and assisted on at least 10, with as many as those 10 as possible being on a supply league.
To be nominated candidates need to have passed a fitness test, which is running at least 2,600m in 12 minutes followed by two 50m sprints each in under 7.5 seconds. If nominated and accepted they have to pass this fitness test again in June or July prior to the season commencing, and also have to attend an FA seminar at which they must pass a laws of the game exam.