If your Macbook's battery has been charging for a while…and it still hasn't charged up even a little…then yes I would say you need a new battery.
As to where to purchase a new battery. It depends on what 2009 MacBook you have. There were two versions released in 2009. One with a easily user replaceable battery…and one with a less-easy to access battery.
Of course you could get one from Apple (the easily replaceable type) like this:
Rechargeable Battery - 13-inch MacBook (White) - Apple Store (UK)
…but you may find that spending £109.00 for it a bit expensive for a 6 year-old computer (maybe…maybe not).
If it's the "technically" non-user replaceable battery. These are not as easy to find…especially if you want a suppler inside the UK. eBay would probably be my first suggestion for either battery. But if you find replacement batteries for far less £££ on ebay than Apple charges (which of course you will). Keep in mind that you get what you pay for. Cheaper build quality…probably less runtime on a full charge…and possibly safety.