Flowerybeanbag is much better at this stuff than me. Maybe she'll be along at some point. For now, here's my perspective.
You say that your current hours are 7am until 6ish. You wanted to work 8-5. How did your flexible working request deal with the work outside those hours? What were your proposals?
The important thing to remember in terms of getting a request accepted (or, if it isn't, hopefully having a decent claim) is that you have to be able to explain how your job will get done during the hours you propose.
In some cases, this might be that a reduced client load = fewer hours. GPs or dentists are good examples of this. They have a set number of appointments per day so it is easy to reduce hours. You just book fewer appointments. It is also dead easy to job share, because chronic conditions which require consistency from one appointment to the next will schedule round your hours and urgent appointments won't expect to see the same person each time.
I don't get the impression that trading is like that. The friends I know in the area spend the time that the market is open trading and the early and late sections doing the admin. Is that you? If so, what happened to that under your proposal? An employer will not agree a request that relies on existing colleagues picking up your work when you go home (and, quite brutally, quite right too. They have lives too, even if they don't have young children). What was your plan for that work?
I apologise if you covered all of this in your request. I may be covering old ground. By IME, far too many flexible working requests rely on the requestee (is that a word? Probably not) getting the flexibility and no real proposals for what happens to other duties.
I also agree with what others have said. Don't focus on your length of service or your personal needs. These are not your employer's concern. Especially in the City, they would quite frankly prefer it if none of their employees had personal lives. Focus on how working part time will make you a better, more productive employee and how you will fit seemlessly into the team on your part time hours.
I also agree that it is good to be as flexible yourself as possible. Can you offer to check emails from home after your child is asleep (if this would help)? can you have a home office to do your hour 5-6 sometime later in the evening?
I am sorry if any of this sounds harsh. It really isn't meant to. I also apologise if you've thought about all this (I mention it because so many people I see haven't) But if you want to put in a decent appeal (which is the next step if you haven't been granted your request) you need to have answers to all of these issues.