Unless you have really nosy neighbours I don't see the issue in her staying with you - she could be a family member like a sister or even your wife - just tell her to put a ring on her finger! As long as you aren't doing anything illegal in public and she is only here a week I doubt it would be an issue. I think you can also pay for the visa with cash - not sure how much it is but she could probably get the currency from a bank in the UK. Good luck!!!