Do you have any ID with a date of birth and picture on it- student card? It will help as you're a girl BUT they are perfectly entitled to ask for a passport/driver's license only so you would not want to be counting on it whatsoever. Worth a shot but still largely doomed to failure. Get a passport, they last for years and years and they are good for travelling, ID, and they are needed when you get a job. Not exactly something you would regret spending money on. Clubs will ID a lot more than pubs, and I'm not sure about the UK but in Ireland all the best clubs are 21+ anyway so they will absolutely ID.
Money depends on how much you drink, transport, whether the club has an admission fee, and if you like to eat junk food afterwards. In and around £40 should do it.