The bank believes that her particular responsibilities could not be properly carried out if she is not there full-time that its clients will not like the idea and that, by agreeing to her request, it will "open the floodgates" for every other woman in the bank.
Accordingly, it refuses the manager's request and she, in turn, threatens legal action against it. In such a deadlock, what are the employee's rights?
The woman's statutory right is to return to the same job that she was doing before she went on maternity leave, so if she was working full-time this would not give her a right to return to work on a part-time or job share basis.
But she may be able to show that, by refusing her request, her employer has indirectly discriminated against her on the grounds of her sex.
There are various hurdles which she must satisfy to succeed in such a claim. These may include the need to produce statistical evidence to show that more men can comply with the requirement to work full-time in the bank than women, and that she thereby suffers a detriment.
Given recent case law, this may not be difficult. However, even if she can make out a case of discrimination, the bank will have an opportunity to justify the discrimination if it can show that the requirement to work full-time is necessary on objective grounds.
A blanket refusal (a "floodgates" argument) to such a request will not succeed in justifying the bank's discrimination. It must be able to demonstrate that, before refusing, it seriously considered the request and investigated whether that could be accommodated.
Having duly considered it, the bank may be able to justify its refusal to allow her to work part-time if she needs to be working for all of the market's trading hours.
This would be because of her need to be available to react immediately to any changes in the market or for continuity of client liaison. It could also be argued that it is impractical and expensive to hire another part-time employee for the hours that she would miss.
A job share may be more practicable if, for example, it would mean that the position is covered throughout the market's trading hours.
Whether the request is for part-time work or a job share, it will be insufficient if the bank simply says that the proposed arrangement will not work because its clients will not like it.
The bank will need objective evidence, for example, that the clients will not or are unlikely to do business with it if she is not available full-time.
It was thought that the position on requests for part-time working would change as a result of the implementation of the EC Part-Time Workers Directive in the UK.
But, rather than facilitating the move between part-time and full-time work, which is an aim of the directive, the regulations that came into force on July 1 2000 are only concerned with ensuring that there is equality of treatment between part-timers and full-timers.
This means that part-timers must receive the same benefits pro rata on their working hours as full-timers.
The British Government has also published "Best Guidance", however, which contains the advice that requests for part-time work and job shares should be considered seriously. The Guidance does not have any statutory effect, but tribunals may take it into account and so employers are urged to follow it.
The steps which employers should follow in responding to requests for flexible working from employees are, as we have seen, largely common sense.
The reasons for taking these requests seriously are numerous: the skills and qualities which are brought to the workplace by women may otherwise be lost and the cost of recruiting and training replacements can be saved.
Also, statistics show that employees who are allowed to work flexible hours are more productive.
But, if employers are in any doubt as to the benefits of taking the time to follow this advice, they should bear in mind a recent case. A manager was awarded three years' salary after she had been dismissed for refusing to work 16-hour shifts for South African Airways when she had an eight-month-old baby.
Even though each case will differ on its facts, this does highlight the need for employers to take into account their employees' individual circumstances. They should not assume that any apparently reasonable requirements that they have with regard to their employees' working hours must be complied with.
Burying heads in the sand when a request for flexible working is made is no longer an option for employers. A considered and reasonable approach to any such requests is needed to avoid legal disputes and it may also have other benefits.