Mbrcatz's answer is irrelevant and incorrect for the UK (or most of the world for that matter) ..... you've hit the nail on the head, it's all about capital and you need tens of millions to do what you are talking about and the start up costs are HUGE... don't forget you'll need accountants, claims professionals, compliance and complaints officers etc etc BEFORE you can sell a single policy. I reckon you'd do better than a million in staff costs before you collected a penny in premium. (60 staff avg £50k a year..which is laughably cheap staff costing in the UK ins market... for 4 months = £1m)
You also need to be able to cope with a catastrophe from day 1...
an insurer has to be able to survive a 1 in 200 year event. That is.... what is the WORST thing that could happen (even if it happens only once every 200 years). In the case of travel it's usually a epidemic which traps a lot of sick people abroad.
How did the big guys start ? Good question..... most of them can trace their history back donkeys years and raised the capital by issuing shares (and increasing that capital over the years) or in the case of Lloyds forming a syndicate of indivduals willing to risk their personal wealth.
Remember you can't 'borrow' money to do this as a loan or loan stock doesn't count as capital (I won't get into Tier1 Tier 2 technicalities).
So forget all that nonsense about hiring actuaries and lawyers... your best bet would be to approach existing companies (or a Lloyds syndicate) with your idea and say ..... "how much do you want to carry this niche market risk". They have their own actuaries etc and as long as you presesnt a serious proposition in a professional manner they WILL listen to you and it won't cost you a bean. You may get a 'binder' type policy (i.e. a special one written just for you) which allows you to underwite risks (within certain parameters obviously) on their behalf. That way they take an awful lot (though not all of the start up costs away) if your business is successful then in 10 years you'll have enough of a track record to go to market and raise the capital to underwrite the business yourself.
I admire your ambition.... but trust me starting an insurance company from scratch is a non starter... not even banks do it, they buy existing insurers (RBS - Directline etc).
If you are really serious and you want to discuss further, drop me a line I'd be glad to point you in the right direction.