Given the situation you find yourself in and the attitude of your employer, if you leave without notice, there is not a a lot they can do legally, and it sounds like they have bigger problems to worry about.
I do know of cases of people leaving without notice and the company did nothing as it is not worth it.
However, you should consider the practical problems that this may pose for you.
You might find it difficult / impossible to get any outstanding pay or holiday pay.
More seriously, they could delay or refuse to furnish you with a P45 which could cause difficulty with your new job.