Talk

It is usual in a company for people with young children to be given a bit of 'leeway'. Other staff shouldn't really have to pick up the slack on a permanent basis. The conditions of service should apply to everyone but with a bit of discretion from management.

In what way are they 'refusing'? Did they know that the hours would include working until 6pm or on Sundays, when they took the job? Or have the hours changed since they started?

I'm assuming you operate a rota of some sort. Has something changed recently, either in the workplace, or in the homelife of one of the staff?

They knew that they had to work till 6 as they were working till 6 before having children. They refuse to management by saying they have to pick their children up from nursery before 6pm, but then tell staff that their partners could pick their children up but they don't want to work till 6 as that would mean getting home too late.

There is a rota which is 9-6 and 1 in 4 Saturdays/Sunday for the staff with no children and 9-5.30 for staff with children - no Saturdays or Sundays are worked.

Presumably they are only getting paid until 5.30 rather than 6? It's something management have to deal with really.

My employer refused my flexiable working request although it is doable.
How can I write an appeal? Lawyer charge almost £300.00.
Please help

You shouldn't need a lawyer to do the appeal. Did you apply formally and did your company decline the request formally? What reason(s) did they give for declining the request? Be aware though, that just because you believe that a request is "doable" does not mean that they have to agree to it.