Your employer must not breach equality laws (for example equal pay laws) when deciding who gets to participate in this kind of scheme.
Where participation is this kind of scheme is available to full-time workers, it should also be offered to comparable part-time workers unless your employer has good objective reasons for treating part-time workers differently. Those reasons should be about more than just saving money.
Schemes approved by HM Revenue and Customs give some tax advantages, but this is a complex matter. You should get further advice from your local tax office and from the GOV.UK website.