Apologies for not getting back to you sooner, I experienced some temporary connection issues and could not get back on the site until now. All appears to be resolved now so I can continue dealing with your query.
Potentially yes, you would be breaching your contract by not fulfilling the notice period but I will explain your position in more detail below.
If the employee fails to honour the contractual notice period then they will be acting in breach of contract. The employer then has the option of suing the employee to seek compensation for damages resulting from their breach. However, in reality such claims are very rarely made. This is mainly due to the costs and time involved, also the relatively small damages that can be recovered. Also the employer has to show that actual losses have been incurred and often that is not easy to do. So whilst there is no way of predicting whether the employer will take this any further or not, chances are that they will not. A more likely outcome is that the employer refuses to provide a reference in the future or if they do, it could mention that the employee had breached their contract.
It is therefore best to try and negotiate a mutually acceptable notice period that would suit both parties. However, if that is not possible and there is a pressing need to leave early, that is still a possibility, subject to the risks identified above.
Finally, there are circumstances when an employee may be entitled to leave with immediate effect and without honouring their notice period. This occurs when an employer has committed a serious breach of contract first. The whole contract, including the notice periods, then becomes immediately void and the employee would be treated as being 'constructively dismissed'. So if there are reasons to believe the employer has acted in breach of contract, whether a breach of an express contractual term, or other breaches such as bullying, exposing the employee to unreasonable stress, discriminating against them, etc this reason can be relied on in order to leave with immediate effect. You could argue that the way they have acted amounts to such a breach but a tribunal may find that it was not necessarily serious enough.
Finally, the employer cannot refuse to pay you for holidays or pay already due for time worked. If they do then it will amount to an unlawful deduction of wages and you can take the matter further to recover what you are due.
This is your basic legal position. I have more detailed advice for you in terms of the steps you need to follow should they refuse to pay you, which I wish to discuss so please take a second to leave a positive rating for the service so far (by selecting 3, 4 or 5 stars) and I can continue with that and answer any further questions you may have. Don’t worry, there is no extra cost and leaving a rating will not close the question and we can continue this discussion. Thank you