A vexatious claim is one that has no reasonable prospect of success, or the person bringing the claim is a serial litigant or has brought the claim to harass the other party. Being vexatious is conducting your claim in an unreasonable way. The Employment Tribunal (ET) can strike out all or part of a claim or response if it is scandalous or vexatious or has no reasonable prospect of success [ET Rules of Procedure 2013, Rule 37
If the ET considers that any specific allegation or argument in a claim or response has little reasonable prospect of success, it may make an order requiring a party to pay a deposit of up to £1,000 in order to continue that allegation or argument [ET Rules of Procedure, Rule 39
The ET may make a costs order or a preparation time order where it considers that a party (or that party’s representative) has acted vexatiously, abusively, disruptively or otherwise unreasonably in either the bringing of the proceedings (or part) or the way that the proceedings (or part) have been conducted, or any claim or response had no reasonable prospect of success [ET Rules of Procedure, Rule 76
The Employment Appeal Tribunal (EAT) has the power to make a 'restriction of proceedings' order banning vexatious litigants from starting or continuing with proceedings, whether in an employment tribunal or in the EAT itself, without the permission of the EAT. The EAT has to be satisfied that a person has habitually, persistently, and without any reasonable grounds, instituted vexatious proceedings in a tribunal or the EAT, either against the same or different persons, or made vexatious applications in any such proceedings. If an order is made against a person, they will have to get the EAT’s permission to start or continue any claim, or make any application in the ET or EAT. [Employment Tribunals Act, section 33
This is what happened to Mr Groves in Her Majesty's Attorney General v Groves
, who made 19 claims in 5 years and Mr Iteshi in Her Majesty's Attorney General v Iteshi
 who made 30 claims in 4 years.