1. All these people are actually offering to sell you is a change of name by deed poll, so that "Lord" would become your new first name. It wouldn't be a title, any more than the "Duke" in Duke Ellington is a title. Given that you can change your name yourself by simply writing out your intention to do so and getting a friend to sign and witness it (see the link) and any home printer can produce a certificate looking as good if not better than that, you'd have to be a prize sucker to pay them their asking price.
It is legal - the sellers are correct that under English law you can call yourself anything you want, provided it isn't fraudulent (or obscene, or a few other things). And obviously, once you have officially changed your name to "Lord Dillon Hopelessly-Gullible" you can, indeed you must, put that on your passport and driver's licence and other legal documents, because that is now your name.
(Why stop at "Lord"? Why not change your name to "Saint Dillon Hopelessly-Gullible"? Or "Pope" or "King"? They would be just as legal.)
You ask "will it work"? Well, it would work in the sense that you would have genuinely changed your legal name, even though you would have spent an entirely unnecessary amount of money doing it. What it would not have done is made you a lord - you'd just be some guy whose name was "Lord". If you wanted people to believe you were a real lord you would, in addition, have to do a lot of lying. And even then, unless you're a talented liar not many people would be fooled.