My name is ***** ***** I'm a US attorney.
If you were still in the US and the company wouldn't pay you the refund to which you are clearly entitled, you could sue them in small claims court, where you could represent yourself and not have to pay legal fees. But you're not, and you're certainly not looking to pay thousands of pounds to mount an international suit to collect $100 USD. The most direct means of recovery is closed to you.
You can file formal complaints with various US consumer rights agencies, however. That may be successful and won't cost you any money. Even if you don't get the $100 back, you would at least tarnish this company's business reputation and make them susceptible to government action if other persons' complaints show a continuing unethical or illegal course of conduct.
File a complaint with the Better Business Bureau at bbb.org. The BBB is a non-profit consumer watchdog agency which for over 100 years has been helping to protect US consumers. A poor review and rating by the Better Business Bureau can cost a company business.
Most companies wish to stay in the good graces of the BBB. The BBB can often mediate in a business/consumer dispute and bring the matter to a mutually satisfactory resolution. They will do this for free, if the company is willing to work with them on your behalf.After that if you get nowhere, you should file a consumer complaint report with your former state Attorney General's Office and also with the Federal trade Commission.
These last two agencies may not intercede to do anything directly for you. But as I have indicated, when the complaints about a business reach a certain level, a government investigation is initiated. When the government finds fraud and/or a pattern of unethical business and marketing practices, they can and do bring a company to Federal court and fine and sanction them. The fine monies received get distributed to consumers who were defrauded by the business. So filing a complaint affects the company and may get you some delayed returns.
I started to add a paragraph about sending a formal letter on legal letterhead, but I figured that even that might cost you the $100 you hope to get back, so in the end I deleted it.
A letter on legal letterhead has no real legal force. But it shows that you have sought out a professional about taking eventual action, so frequently it is an effective means to an end. A reasonable company would give you a refund rather than risk suit.
If it does not work, you would NOT have to actually sue if you do not wish to.