I am currently in London on BUNAC.
To clarify some of the questions:
Regarding the bank account, BUNAC has an arrangement with the Aldwych branch of Natwest in London. To open it you need your passport, BUNAC Blue Card, 100 pound minimum deposit, a bank reference letter from your home bank saying you are a customer in good standing, and the letter that BUNAC provides for you. You also have to set up your appointment through BUNAC's office (all covered in the pre-departure information and the mandatory BUNAC orientation upon arrival.) However, once it is opened, you obviously can bank at any Natwest branch, just change your address - you have to open the account using BUNAC's hostel address, but BUNAC forwards all bank mail onto you for free. I opened this account quite easily, and the only thing I don't like about it is that it only provides a Solo card (not accepted everywhere) - but was very simple to open.
For the NIN, BUNAC provides you with the number to call and information on what you need to apply, but applying for it is entirely up to you.
My home insurance company does cover me - but it does vary. BUNAC offers insurance at a fairly reasonable price if I remember correctly. (Around US$350 for 6 months?)
You need to have "access" to a minimum of 1000 pounds, not bring it all in cash or travellers cheques. They didn't ask me about finances at all at immigration, but they certainly have the right to see that have access to this amount. Personally, in addition to my bank statements, I brought over a letter from my mother stating she would provide me with funding if needed (but obviously wasn't asked to see this.)
To sum up, BUNAC has been a great option for me. Complete freedom in where to work or live, but with the right amount of support in helping get bank details and other things sorted. Their office in London is full of helpful information and listings, and the people working there are very friendly and helpful as well.
Any more questions, feel free to ask!