There is little to lose by adopting that approach and I would hope they will eventually agree to your request rather than lose you over it.
As far as flexible working is concerned, The right to make such a request applies to any employee who has been employed by the employer for at least 26 weeks and is limited to one request in any 12-month period. Examples of the changes that can be applied for in a flexible working request include changes to working hours, times and work location.
Once an employer receives a formal request they must deal with it in a reasonable manner, ideally meeting with the employee to discuss it and, if rejected, communicate their decision within 3 months of the date the initial request was submitted. When rejecting the request, the employer is only able to do so by relying on any of the following grounds:
· Planned structural changes
· The burden of additional costs
· A detrimental impact on quality
· The inability to recruit additional staff
· A detrimental impact on performance
· The inability to reorganise work among existing staff
· A detrimental effect on ability to meet customer demand
· Lack of work during the periods the employee proposes to work
Ideally, the employer should also try and explain their decision in writing, such as providing information on why they believe the selected reason for rejection is relevant and they have relied on it.