Not sure which text Handel's librettist might have used as a starting-point for his Giulio Cesare, but an obvious beginning point would be Plutarch's Life of Pompey as translated by John Dryden:
[H]e passed over sea without danger. But on hearing that king Ptolemy was posted with his army at the city of Pelusium, making war against his sister [i.e., Ptolemy's sister, Cleopatra], he steered his course that way, and sent a messenger before to acquaint the king with his arrival, and to crave his protection. Ptolemy himself was quite young, and therefore Pothinus, who had the principal administration of all affairs, called a council of the chief men, those being the greatest whom he pleased to make so, and commanded them every man to deliver his opinion touching the reception of Pompey. It was, indeed, a miserable thing, that the fate of the great Pompey should be left to the determinations of Pothinus the eunuch, Theodotus of Chios, the paid rhetoric master, and Achillas the Egyptian. For these, among the chamberlains and menial domestics, that made up the rest of the council, were the chief and leading men. Pompey, who thought it dishonorable for him to owe his safety to Caesar, riding at anchor at a distance from shore, was forced to wait the sentence of this tribunal. It seems they were so far different in their opinions that some were for sending the man away, and others again for inviting and receiving him; but Theodotus, to show his cleverness and the cogency of his rhetoric, undertook to demonstrate, that neither the one nor the other was safe in that juncture of affairs. For if they entertained him, they would be sure to make Caesar their enemy, and Pompey their master; or if they dismissed him, they might render themselves hereafter obnoxious to Pompey, for that inhospitable expulsion, and to Caesar, for the escape; so that the most expedient course would be to send for him and take away his life, for by that means they would ingratiate themselves with the one, and have no reason to fear the other; adding, it is related, with a smile, that “a dead man cannot bite.”
This advice being approved of, they committed the execution of it to Achillas. He, therefore, taking with him as his accomplices one Septimius, a man that had formerly held a command under Pompey, and Salvius, another centurion, with three or four attendants, made up towards Pompey’s galley. In the meantime, all the chiefest of those who accompanied Pompey in this voyage, were come into his ship to learn the event of their embassy. But when they saw the manner of their reception, that in appearance it was neither princely nor honorable, nor indeed in any way answerable to the hopes of Theophanes, or their expectation, (for there came but a few men in a fisherman’s boat to meet them,) they began to suspect the meanness of their entertainment, and gave warning to Pompey that he should row back his galley, whilst he was out of their reach, and make for the sea. By this time, the Egyptian boat drew near, and Septimius standing up first, saluted Pompey in the Latin tongue, by the title of imperator. Then Achillas, saluting him in the Greek language, desired him to come aboard his vessel, telling him, that the sea was very shallow towards the shore, and that a galley of that burden could not avoid striking upon the sands. At the same time they saw several of the king’s galleys getting their men on board, and all the shore covered with soldiers; so that even if they changed their minds, it seemed impossible for them to escape, and besides, their distrust would have given the assassins a pretence for their cruelty. Pompey, therefore, taking his leave of Cornelia, who was already lamenting his death before it came, bade two centurions, with Philip, one of his freedmen, and a slave called Scythes, go on board the boat before him. And as some of the crew with Achillas were reaching out their hands to help him, he turned about towards his wife and son, and repeated those iambics of Sophocles—
“He that once enters at a tyrant’s door,
Becomes a slave, though he were free before.”
These were the last words he spoke to his friends, and so he went aboard. Observing presently that notwithstanding there was a considerable distance betwixt his galley and the shore, yet none of the company addressed any words of friendliness or welcome to him all the way, he looked earnestly upon Septimius, and said, “I am not mistaken, surely, in believing you to have been formerly my fellow-soldier.” But he only nodded with his head, making no reply at all, nor showing any other courtesy. Since, therefore, they continued silent, Pompey took a little book in his hand, in which was written out an address in Greek, which he intended to make to king Ptolemy, and began to read it. When they drew near to the shore, Cornelia, together with the rest of his friends in the galley, was very impatient to see the event, and began to take courage at last, when she saw several of the royal escort coming to meet him, apparently to give him a more honorable reception; but in the meantime, as Pompey took Philip by the hand to rise up more easily, Septimius first stabbed him from behind with his sword; and after him likewise Salvius and Achillas drew out their swords. He, therefore, taking up his gown with both hands, drew it over his face, and neither saying nor doing anything unworthy of himself, only groaning a little, endured the wounds they gave him, and so ended his life, in the fifty-ninth year of his age, the very next day after the day of his birth.
Cornelia, with her company from the galley, seeing him murdered, gave such a cry that it was heard to the shore, and weighing anchor with all speed, they hoisted sail, and fled. A strong breeze from the shore assisted their flight into the open sea, so that the Egyptians, though desirous to overtake them, desisted from the pursuit. But they cut off Pompey’s head, and threw the rest of his body overboard, leaving it naked upon the shore, to be viewed by any that had the curiosity to see so sad a spectacle. Philip stayed by and watched till they had glutted their eyes in viewing it; and then washing it with sea-water, having nothing else, he wrapped it up in a shirt of his own for a winding-sheet. Then seeking up and down about the sands, at last he found some rotten planks of a little fisher-boat, not much, but yet enough to make up a funeral pile for a naked body, and that not quite entire. As Philip was busy in gathering and putting these old planks together, an old Roman citizen, who in his youth had served in the wars under Pompey, came up to him and demanded, who he was that was preparing the funeral of Pompey the Great. And Philip making answer, that he was his freedman, “Nay, then,” said he, “you shall not have this honor alone; let even me, too, I pray you, have my share in such a pious office. that I may not altogether repent me of this pilgrimage in a strange land, but in compensation of many misfortunes, may obtain this happiness at last, even with mine own hands to touch the body of Pompey, and do the last duties to the greatest general among the Romans.” And in this manner were the obsequies of Pompey performed. The next day Lucius Lentulus, not knowing what had passed, came sailing from Cyprus along the shore of that coast, and seeing a funeral pile, and Philip standing by, exclaimed, before he was yet seen by any one, “Who is this that has found his end here?” adding, after a short pause, with a sigh, “Possibly even thou, Pompeius Magnus!” and so going ashore, he was presently apprehended and slain. This was the end of Pompey....except in the Met version, Tolomeo gets to take the final curtain with the victors, bloodied but otherise no worse for wear. Poor Pompey's head remains in its box.
Not long after, Caesar arrived in the country that was polluted with this foul act, and when one of the Egyptians was sent to present him with Pompey’s head, he turned away from him with abhorrence as from a murderer; and on receiving his seal, on which was engraved a lion holding a sword in his paw, he burst into tears. Achillas and Pothinus he put to death; and king Ptolemy himself, being overthrown in battle upon the banks of the Nile, fled away and was never heard of afterwards. Theodotus, the rhetorician, flying out of Egypt, escaped the hands of Caesar’s justice, but lived a vagabond in banishment; wandering up and down, despised and hated of all men, till at last Marcus Brutus, after he had killed Caesar, finding him in his province of Asia, put him to death, with every kind of ignominy. The ashes of Pompey were carried to his wife Cornelia, who deposited them at his country house near Alba.
Afterthought: well, what makes you think he would use an English source? The libretto is in Italian, not so? So how about an Italian source? Or, while we are at it, the original Greek?