Pretty much everything you need to know is in these three posts.
https://bitcointalk.org/index.php?topic=314402.msg7931395#msg7931395https://bitcointalk.org/index.php?topic=314402.msg7290648#msg7290648https://bitcointalk.org/index.php?topic=314402.msg7293210#msg7293210What anderl said is correct and has been pointed out before. HMRC do not classify mining as a business activity it can be done as an individual and profits treated as a Capital Gain not income. Their claim is an outright lie and an idiot could tell their T&Cs were "typed up" by a clown
Regarding Lawyers. Why waste your time when you can get every penny back through small claims online for as little as £70? If you want to try and coordinate a complicated class action across multiple counties over the internet by all means give it a try. But by the time you get to court, Alpha will probably have folded and disappeared with your money. Personally I'd just pay the £70, have a Judge rule on it, and get my money back all from the comfort of my computer desk. But its up to you.