I'm not a lawyer, so wait for one to pass this way — but in the meantime...
Did they give you Terms and Conditions when you first opened an account with them? Do you have anything that could constitute a contract? What does it say? Is there any paperwork that says they can and will do this? If they have a website does it say anything about their terms on there? Is there anything that says that once money has been paid into an account it will be non-refundable? Is there anything indicating that credits to your account are classed as Gift Vouchers?
If not, and if I don't have their T&Cs, I'd start by asking them for a copy and then ask, if they supply them, why they didn't give them to you when you opened an account. Even if the T&Cs do turn out to say that refunds aren't allowed, you should have had a copy so that you had the opportunity to apprise yourself of your rights before you put money into the account. Two or three calmly worded letters pointing out that they don't have a leg to stand on should see results.
If not, and if you're sure you have a case against them, threaten them with the Small Claims Court and if they still don't cough up, lodge a claim. It'll cost you £35 and if they're wise they'll pay back the £100 and the £35 and not bother wasting their time turning up for court.
You could use social media to apply pressure. Something factual along the lines of: 'Just a word of warning about this business, they don't offer refunds once you've paid money into your account with them. They don't tell you that when you create an account and I've lost £100' might do the trick.
You could also contact one of the many Consumer Champions in the national press. Most newspapers have a column where a consumer expert tries (and often succeeds) in sorting this kind of situation. They will sometimes pick a generic problem such as this, even if the monetary value is low, because they know it may help a wide range of people with a similar problem.