A conventional view is that your current employer is not expressly legally required to provide a reference to your new employer.
However, it may be under an implied duty, especially where it is customary to supply a reference in a particular industry or for particular types of employee. In addition, failure to provide a reference as a form of retaliation, for example because an employee has brought, or threatened to bring, a discrimination claim against the employer, may amount to victimisation. In this circumstance you would be entitled to bring a claim to an employment tribunal with a view to seeking a declaration and compensation.
Where a reference is given, the employer has an implied duty of care to both the former employee and the prospective employer. The reference must be accurate and compiled with care. You may be able to bring a civil case for negligence if you suffer damage as a result of an inaccurate reference (e.g. the unjustified reference causes a job offer to be withdrawn).
However, where a reference is provided your employer also has a duty of care to provide relevant and accurate information to the prospective employer, even if such information is unfavourable to you.
In practice most employers now only offer simple references: “x worked as y between the dates of a and b”. This used to be considered tantamount to a bad reference but is now widely accepted – although less so in the public sector where ex-employers are often asked to complete a form with a series of questions about your employment.