My uncle is a Road Traffic Enforcement Bailiff, he deals with unpaid parking fines all the time. The original fine is £50, if you continue to refuse to pay the price escalates more and more with court fees and bailiff fees. The average £50 parking ticket is at about the £400 mark by the time it gets to the Bailiff.
You are fully within your rights to appeal. However, what I would suggest you do is pay the fine whilst it is still at the £50 mark, then appeal. If you get nowhere for whatever reason, it's only £50, whereas if you refuse to pay and drag it out with an appeal, the debt will be at £400 before you know it, and there's nothing you can do it but pay, the Bailiff is issued with a warrant from the county court (Northampton County Court currently deals with all Road Traffic offences) which gives them the right to remove goods to the value of the debt if the debt isn't paid. This in itself incurrs about £120 in fees on top of the £400 for the van to be called out. They can take anything from your home address that is yours, this includes cars and everything but clothes, bedding, one table, one chair and something to cook with. On a £500 debt they will more or less clear your house out as even the most hi-tech electrical equipment fetches bugger all at auction. That's just to give you a bit of an incite as to what could happen. By the way, when I say things that are yours, it doesn't just mean that. Unless other people in the household can prove that they own things, i.e. documented receipts, they can take that stuff too. So if you haven't got the receipt for the TV you bought a year ago, tough ****.
So basically my advice is pay the fine at the earliest possible point to avoid any further cost to you should your appeal succeed. I don't know where you will stand with an appeal, the lines weren't visible, however, they are there, so I don't know where you stand to be honest. One thing I do agree on though is that you have no legal right to park even outside your own home unless you own the road like has previously been stated. I think your best bet is to go down the broken yellow line route, however I have a sneaky feeling they've probably changed the regulations slightly what with the Watchdog case.
Good luck to you all the same.