He's the Raven King.
Who else could he possibly be? A magician of great power - enough to revive the dead without fairy assistance - who dresses in black and, as noted in the question, looks like pictures of the Raven King seen earlier. Don't forget, also, that he changed the writing upon Vinculus's body. Vinculus was the personification of the Raven King's book; the writing upon him was the Raven King's prophecy - who but the Raven King could change it to show something new and different?
His description in the book makes his identity all the more clear:
The man wore black boots and a black travelling coat. He was half-stooping, half-kneeling on the snowy ground beside Vinculus. For a brief moment Childermass thought it was Strange –but this man was not quite so tall and was somewhat slighter in figure. His dark clothes were clearly expensive and looked fashionable. Yet his straight, dark hair was longer than any fashionable gentleman would have worn it; it gave him something of the look of a Methodist preacher or a Romantic poet. "I know him," thought Childermass. "He is a magician. I know him well. Why can I not think what his name is?"
Out loud he said, "The body is mine, sir! Leave it be!"
The man looked up. "Yours, John Childermass?" he said with a mildly ironic air, "I thought it was mine."
It was a curious thing but despite his clothes and his air of cool authority, his speech sounded uncouth –even to Childermass's ears. His accent was northern –of that there was no doubt –but Childermass did not recognize it. It might have been Northumbrian, but it was tinged with something else -the speech of the cold countries that lie over the North Sea and –which seemed more extraordinary still –there was more than a hint of French in his pronunciation.
[...]
"Does the land hereabouts belong to you, sir?" [Childermass] asked.
"Yes."
"And where is your horse? Where is your carriage? Where are your servants?"
"I have no horse, John Childermass. I have no carriage. And only one of my servants is here."
"Where?"
Without troubling to look up, the man raised his arm and pointed a thin, pale finger.
Childermass looked behind him in confusion. There was no one there. Just the wind blowing across the snowy tussocks. What did he mean? Was it the wind or the snow? He had heard of mediaeval magicians who claimed these and other natural forces as servants. Then comprehension dawned on him. "What? No, sir, you are mistaken! I am not your servant!"
"You boasted of it, not three days ago," said the man.
-- Jonathan Strange & Mr Norrell, Chapter 67 (emphasis mine)
A mysterious figure with great magical power and a strange accent, who claims to own both Vinculus's body and the surrounding land, and whom Childermass has boasted of serving - come on, there's only one man this can be.
But he didn't come because of Strange and Norrell's summons.
You're right that Strange and Norrell's attempt to summon the Raven King to them failed, and they instead summoned Stephen Black, the new 'Nameless Slave'. But in thinking that they are the ones pulling the strings, that they even had the power to affect the Raven King, you're making the same mistake Childermass did in the book:
"So?" said Childermass, stung. "That is not so very trifling, is it? Norrell is a clever man - and Strange another. They have their faults, as other men do, but their achievements are still remarkable. Make no mistake; I am John Uskglass's man. Or would be, if he were here. But you must admit that the restoration of English magic is their work, not his."
"Their work!" scoffed Vinculus. "Theirs? Do you still not understand? They are the spell John Uskglass is doing. That is all they have ever been. And he is doing it now!"
-- Jonathan Strange & Mr Norrell, Chapter 67
(John Uskglass == the Raven King, of course - I can't remember if that name was ever mentioned in the TV series)
It's the Raven King who is pulling the strings, and has been from the very beginning. It was he, through his prophecy and his agent Vinculus, who brought Strange and Norrell together in the first place. He showed up to resuscitate Vinculus and rewrite the prophecy because he wanted to, not because they attempted to summon him.
In the books, Strange and Norrell actually know that he was in England, even though they never got to see him in person. Like you, they made the mistake of believing that their summoning spell had something to do with his presence there:
Norrell did the magic, naming John Uskglass as the person they sought. He divided the surface of the water into quarters with lines of glittering light. He gave each quarter a name: Heaven, Hell, Earth and Faerie. Instantly a speck of bluish light shone in the quarter that represented Earth.
[...]
In a tone of wonder, Norrell said, "I think we may have succeeded after all! It says he is here. In Yorkshire!"
-- Jonathan Strange & Mr Norrell, Chapter 66
And later on, when he returns to his own kingdom, they reflect on why he didn't come to them despite their summoning charm, the reason for which boils down to "he was too proud":
In the silver dish of water the speck of light flickered and disappeared.
[...] "He is gone," he said. [...] "It is very odd," continued Norrell, in a tone of wonder. "What do you suppose he was doing in Yorkshire?"
"Oh!" cried Strange. "I dare say he came here on purpose to make me mad!" With a cry of mingled rage and self-pity he demanded, "Why will he not attend to me? After everything I have done, why does he not care enough to look at me? To speak to me?"
"He is an old magician and an old king," answered Norrell briefly. "Two things that are not easily impressed."
-- Jonathan Strange & Mr Norrell, Chapter 68
