Ask yourself this question first - what outcome are you looking for?
I know that the ideal answer is probably that the employer rolls over and gives in - but given your recent experience, do you think that this is likely? What is it going to be like to work for under this sort of hassle?
I'm afraid that there are just some employers who don't seem to easily accept the way the law was drafted and intended to work - and they seem bent on making it difficult.
If then, the answer is you would be prepared to accept money to be out of it, then I can understand where you are coming from - lawyers can probably help.
As a first stab, why not try CAB, who may be able to get you to a solicitor for 30 minutes free advice.
I'm not going to apss judgement on what has happened - and don't have enough of the details to be informed enough - but employers do only have to show adequate grounds for why your request for p/t cannot easily work around business needs.
However, from what you also say, the required process of determining this outcome appears not to have been followed. You should know that far more employers fall foul of not following the correct process (and hence lose the case at ET) than make an unfair decision in the first place.