The easiest way to handle this when you don't have any investments, no professional liability or other complications, is simply that you set each your own individual sole proprietorship. Your friend, as he handles the administration, bills the client, and you bill him. Your agreement should likely be that you get paid when he does.

This way, if things turns sour, you only stand to lose what your friend owe you - there's no legal entity that you share and might need legal help to dissolve. If you don't trust your friend to make such a setup (even if this particular setup isn't the right one), you shouldn't go into business with him.

Regarding the rate, don't undersell yourself. There's an expectation as to what a professional developer costs (probably way closer to £70/hr than £25/hr), and if you don't meet that expectation (in either direction) you'll experience some friction. You can give a one-off discount, e.g. as a voucher handed out as marketing. Underbidding is for punks with ASP.net for dummies and "Hello world" under their belt, bidding at the actual price is what professionals do. State your rate at what you think you're worth, and be prepared to give a discount if you feel it's the right thing to do. That way the client also feels like he got something.