I can just hear the in-flight chatter..."...and rolling left...lipstick on, GO!"
The RAF traditionally had front-line fighter squadrons as display teams, going back to before World War Two. Douglas Bader flew the Bulldog in such a team, and it was in one of these that he crashed and lost his legs during an 'unofficial' singleton display at a flying club visit.
In the 1950's, the famous 'Black Arrows' of 111 Squadron carried on this traditon for a couple of years, flying black-painted Hunters, and 92 Squadron followed with all-blue Hunters. When the Lightning became the front-line fighter, both 111 and 56 Squadrons fielded display teams, 56's Lightnings carrying a striking red livery on the fuselage spine and fins, with the 'Firebird' motif and red and white Squadron checkers prominent.
There was then a move to free the squadrons from this task, in order to allow them to fully perform their true tasks as Air Defence of Great Britain, as the training and peparation for the 'display season' took a lot of time and, of course, the expense associated with keeping a number of service aircraft tied up with what was, essentially, PR work.
The role fell on the Central Flying School, with a number of teams formed from top-class instructors, flying the Jet Provost (The Pelicans) and also the then new Folland Gnat trainer, the latter team known as 'The Yellow Jacks', due to the overall yellow colour scheme then used on this tiny jet. Eventually, the team became the official Aerobatic Team of the RAF and, with overall red-painted Gnats, the title of 'The Red Arrows' was born. When the BAe Hawk replaced the Gnat in the advanced trainer role, the 'Arrows' of course converted to this type, which they have used ever since, still flown by very experienced instructors, or high-hours pilots, who normally have a three year tour, the first year being spent as a sort of 'apprentice'.
Front-line aircarft are still displayed in the RAF, with one, or sometimes a pair of fighters from a particular squadron carrying out that role for a year or two. These would include, for example, a Tornado GR variant, and, as with 56 squadron before being disbanded and re-forming in the ECM role, the Tornado F3 representing the fighter variant. These are/were flown by squadron crews, as a secondary duty, meaning they had very little, if any, free time during their tenure as display crews. This is also true of the pilots in the BBMF, who are drawn from the OCU or Squadrons for the Spits and Hurricanes, and from multi-engined aircraft squadrons for the Lancaster and Dakota, with only the OC BBMF being a full-time posting as far as air crew are concerned.