Subject to the disclaimer that I'm not a lawyer / payroll expert / bank employee...
I don't think so. (I'm assuming we're talking English law here)
It is not legal to withold wages for work already done (i.e. up to whatever the last working date was) if someone leaves without working their proper notice.
I would have thought it would be in order to request the wages for the period not worked back, and pursue this through the court if they don't pay up. I'd say polite-ish letter, firm letter sent recorded, then court.
(I'm not sure whether this sort of thing would be through 'small claims' or whether it's the sort of thing an employment tribunal would cover. I think if a firm fails to pay wages, you go to employment tribunal first. Not sure how it works the other way.)
It would (as far as I'm aware) also be lawful for an employer to seek reimbursement for things like training costs, any tools / equipment an employee fails to return on leaving - as long as this has been put in writing in the contract of employment / any supplement to it.
I am not quite sure where anyone would stand when it came to outstanding holiday pay / holiday pay owed if the employee has already taken some of the leave they would accrue in following months.
I guess this is a risk employers take if they pay much before the end of the month.
I believe there is case law for employers taking an ex employee to court for damages if they fail to work out their notice, but the employer would have to prove specific losses (e.g. loss of business, hiring expensive consultants to do the work) - broadly speaking this is only going to be viable for a fairly high-up employee.
In terms of references, there is an urban myth that it's now illegal to give "a bad reference" - this is cobblers, but someone can take an ex employer to court if a reference is false or malicious. Some employers have decided to avoid any possible risk by giving only references that confirm dates of employment (although such references are not accepted by all potential employers...)
Assuming you're the employer here, are you aware that
www.acas.org.uk have a telephone advice line that any employer or employee can ring to chat something through?