The documents you need to apply for a visitors visa are the same kind of things you would need if you just show up at the border. The benefit of this is that generally folks will apply for their visa before making travel arragements, but in your case, I'm afraid you will be out the money you spent on the plane ticket no matter what since your travel insurance will most likely not cover you in this instance.
This is from the ukvisas.gov.uk site:
What supporting documents should I include with my application?
You should include all the documents you can to show that you qualify for entry to the UK as a visitor. If you do not, we may refuse your application.
As a guide, you should include:
- bank statements, payslips, or some other evidence to show that you can pay for the trip and that you have enough money to support yourself and any dependants without working or getting any help from public funds, and
- evidence that you intend to leave the UK at the end of your visit (for example, a letter from your employer).
If you are visiting family or friends you will need:
- a letter from your sponsor (the person you are visiting) explaining your relationship with them and the purpose of your visit, and
- a copy of the bio-data page (the page containing their photograph) of their UK passport or, if they are not a UK national, evidence of their immigration status in the United Kingdom.
If your sponsor will be supporting you during your visit, or paying for the cost of the visit, you will need:
-payslips, bank statements, or some other evidence to show that they have enough money to support you.
We will refuse your application if we find that any documents are false.