Verbal contracts as far as employment law are concerned in the UK are binding.
Verbal contracts can be legally binding in the US as well. The only problem is, how can you prove in court what was verbally discussed, verbally agreed to, etc. How can you demonstrate that the employer made the request for at least 2 weeks notice, and that the employee actually agreed to that request? Also, typically for any contract to be legally binding both parties have to offer some form of consideration. What does the employee get in return for agreeing to give two weeks notice? And of course, was all of this clearly explained verbally and agreed to before the person was employed, or was he only told it after the fact? If it was after the fact then it probably would not be legally binding, and since it is a verbal contract it's going to be next to impossible to prove/disprove what someone said, let alone when they said it.
I would not hire someone who left their previous position without sufficient notice unless I knew the previous and future employers had worked out the issue before setting a date.
And how, pray tell, would you know that? A candidate could tell you whatever he wanted, and you would have little choice but to believe him. A disgruntled manager could simply lie when you call and ask for references. Maybe they think that if they can make the candidate look bad then they won't be able to get another job and leave. Frankly, you have no way to be sure what sort of notice the candidate provided their employer or what sort of arrangements were made for a transition period. More to the point, it's none of your business, ethically or legally. It is impossible to know the true circumstances.
I would also mention in references that the person did not give sufficient notice before leaving their position.
You certainly could do that, but in the US you could very well be opening yourself up to legal action if your negative report affected their employability. Again, it comes down to what you can prove, and you can't prove anything definitively. More to the point, what constitutes sufficient notice? In "at-will" employment states, there is no legal requirement to give notice, it is merely a courtesy. Providing someone with a negative reference for failing to comply with your "company's own internal policy" when that policy is clearly contradictory to employment law could certainly be actionable.
That's why in most cases (again, in the US) you have to be very careful about giving and getting references. At most companies (at least those with competent HR and legal departments) they require that all employment verification requests go through HR. Typically they'll only verify factual statements that can't be disputed, like your dates of employment, starting position, last position held, and in some rare cases, salary level.
The only other question that sometimes comes up is "are they eligible for rehire?" Getting "no" to that answer could mean that they were fired for cause, or left on bad terms, didn't give the kind of notice period that the company wanted, etc. But they don't go into details for fear of being sued. The definition of "sufficient notice" varies widely as well. Most companies in the US would say two weeks. I've worked for one that said 4 weeks was the minimum sufficient notice. In fact, I was working for a company that had a 2-week notice standard that was bought by a 4-week notice company. Where does that leave me? I agreed to give 2 weeks notice when I hired on, but suddenly the game was changed after 3 years of service. A company could get really crazy and require 16 weeks notice AND hold vacation pay or other benefits hostage (depending on how vacation time is given this may or may not be legal, but most people wouldn't challenge it).
Let's go a step further and talk about consultant firms. I'm an employee of a consulting company that contracts me out for projects and other work of varying lengths. Sometimes I'm doing work on a T&M basis that's only supposed to last a week. Sometimes I'm doing work on a long-term project that could run 6 months or more. That project could be billed on T&M for a specific deliverable or on a fixed cost basis, whatever. If I'm only working on small projects then 2 weeks might be sufficient notice to finish them. If I'm working on a 6-month project and it's only 2 months into it, then is 2 weeks still sufficient, or do I need to give 4 months notice? Keep in mind that I am assigned to projects rather than getting to pick and choose. How can notice that would be sufficient one month not be considered sufficient the next? Could my employer make my life hell by continually assigning me to overlapping 6 months projects that make it impossible to give reasonable notice? That makes it pretty difficult to leave a company.
How many employees actually know what the "sufficient notice" period for their new employer is before they've quit and started the new job? Usually that sort of info is in the company handbook, which you get in orientation on the first day of work. How can you expect to hold someone to that standard when they don't even know what the standard is when they get into it? The point is, the notion of "sufficient notice" can be (and is) abused by employers, and it's hardly grounds for disqualifying a candidate.
Companies invest a great deal of money to train their employees; while I do not expect employees to thank the company for that, I do expect them to show respect and not dump all of their tasks on a coworker when they choose to accept a new position.
Not all companies invest "a great deal of money" to train their employees, and not all companies treat their employees with respect. While you may work for a great company that does everything right, you have no way of knowing what sort of company the candidate is coming from.