From Private Investigators UK:
Polygraph testing is 100 per cent, totally, completely legal in the United Kingdom. However, there are a few conditions. The person undergoing the polygraph exam must be cooperative and willing to take the polygraph. No one can be forced to take one. The person administering the polygraph test must be qualified to do so and must hold a relevant degree and license. These results however, are inadmissible in a court of law. This is because there is a fair chance of the results of a polygraph being inaccurate. Since physiological responses are measured, it is possible that the stress of the situation may cause the examinee to register many false positives.
As the results are inadmissible in a court, I think there would be reasonable grounds to claim unfair dismissal if she were sacked because of the test's results.