Guidance was issued by the Information Commissioner's Office (ICO) in May 2013. Under Section 14 (1) Freedom of Information Act 2000, public authorities do not have to comply with vexatious requests. It is the request which is vexatious, not the individual making it!
In cases where the issue is not clear-cut, the key question to ask is whether the request is likely to cause a disproportionate or unjustified level of disruption, irritation or distress.
Vexatious = “manifestly unjustified, inappropriate or improper use of a formal procedure”
See the complete guidance on the ICO website