SR71,
The engagement freeze is just the name of the type freeze you get on joining the company and it lasts for 5 years. The difference between it and a subsequent type freeze you get from bidding to a different fleet is that during the engagement freeze you can be moved by BA to any posting at their whim, after 5 years in the company you only move fleets by placing a bid (and being senior enough and there being a vacancy on your new fleet, of course.)
If you do have a successful bid (freeze waiver granted by BA for whatever reason) you are re-frozen for the greater of the rest of your engagement freeze OR the new freeze on type. That's not really applicable now since type freezes are longer than they once were.
The freeze periods are very approximate anyway as they apply only to the "training year" which starts on the 1st June. This means a pilot who starts a course on 2nd of June 2003 and another who starts his course on 30th May 2004 will both have completed one year of their freeze period by 1st June 2004 despite the first pilot having served a year more than the other.