I lost 3st in 21 weeks. I stuck to the plan like glue and exercised like a demon, including a week at a bootcamp abroad where I lost 8lbs, which definitely spurred me on. It can be done, but totally depends on each person - how quickly they lose, how well they stick to plan, what exercise they do, and what motivation they have. I would also say, I was over 16st when I started. The first 4 st came off quickly, but my weight loss has slowed down since then.
I had a goal in mind that I was determined to lose the 3st for. Keep your family holiday and the 3st goal in your head as something to work towards, but don't be disappointed if you don't reach it. If you stick to plan, you will still lose, and, whether you hit your 3st goal in 23 weeks or not, all losses are an achievement.
Good luck!