Thank you for your message.
First check the Company Articles. Sometimes, albeit rarely, these have a built in answer for this type of problem. However, if that does not address the particular problem, there there is always a legal way. The legal way out of this mess may also mean costs to both sides and will without a doubt end up in the business folding long before the dispute gets near a court room.
The option really is either:
(a) one party buys the other out; or
(b) wind up the business and each goes their separate ways.
Now, either the court can enforce one of the above two options (see time, effort, cost, business failure above). Or, the parties can sort it out themselves.
Usually, due to the bad blood between the partners, no sensible solution can be achieved in practice, unless they appoint either solicitors or other middlemen (eg accountants) who can talk sensibly without mud-slinging and personal attacks.
In fact, to help further, there's an almost foolproof way of deciding right away which of the above two options is the answer. It usually goes by (a) if the company has any value left, and (b) if it doesnt.
Finally, a decent solicitor should explain the costs of legal fighting up front, and its surprising how that can concentrate the mind to sorting out an otherwise 'intractable' problem!