I think it's achievable to get out but requires careful planning and an enormous amount of sherry. Essentially you need to combine two things: 1) get everyone attending your Christmas lunch violently drunk, even children and babies. 2) engineer a massive family dispute. Here, it's vital that you emerge from the row as the injured, wounded, profoundly hurt party. So much so that it all gets too much and you simply have to storm out, for air and a chance to regroup. This is where planning is vital which means the car must be packed with your stuff including appropriate clothing. Suspicions will be aroused if you storm out and then a few minutes later storm back in for your fishing tackle and bait.
Don't dive straight in with the emotional hand-grenade- build up to it. Maybe start with hiding the potatoes or a key present for a visiting aunt. Build the tension and animosity. Subtle references to past family events- when uncle Clive was caught "entertaining" some midgets in his garden shed for example. But for god's sake don't come straight out with it. Just make sure an innocent sentence contains the words "Clive" and "midget". Not easy that, hence the need to plan. Another way to set shi* off, is by interfering with those stupid jokes or proverbs that you get in crackers. Replace them with your own. Again, don't go for the jugular here, be subtle and don't draw a picture of a man in a shed with a midget. You could mime it though in a game of charades.
The other key to this is the sherry. Be the good husband/uncle/grandfather and make up baby Clive's milk. A ratio of 5:1 for milk and sherry should do it. You can reverse this if baby looks unaffected by its consumption of alcohol (it's obviously hard to tell given they stagger about and bump into stuff anyway). Ideally you want them violently sick because that, combined with being offended so badly by the massive family dispute, creates a fantastic diversion allowing a safe exit.
I should confess right now that I only ever got to try this technique once.