Henry I took five years to get around to the business of appointing a new archbishop, for motives William impugns:
After Anselm of venerable memory had escaped the captivity of his body of clay and bidden farewell to this life, his see was vacant for a full five years... All this time, whenever the king was warned to look to the widowhood of his mother the church, he put his advisors off with a bland reply: the archbishops sent by his father and brother [i.e. Lanfranc and Anselm, chosen by William I and William II respectively] had been of high quality, and he was unwilling to fall short of the good fortune of his relatives; there was therefore need of careful consideration to make sure he put in place an archbishop who equalled or came near to the virtues of his predecessors.
Replies like this seemed entirely lawful and proper, but a pile of money kept the king's mind happy, and cured the unease with which others regarded the delay. Finally, when he could not put it off any longer without almost irremediable scandal, the king assembled a council at Windsor, intending to bring the matter to a conclusion.
Amusingly, in the process of revision William emended this last paragraph to: "Replies like this seemed entirely lawful and proper, and indeed they were. So after long and anxious discussion, the king assembled a council..." Do you believe him? I don't!
[The king's] intention was that the choice should fall upon Faricius abbot of Abingdon, a man of great severity, together with remarkable energy in carrying through his plans. The king, however, did not insist on having his own way, at least in the choice of archbishop, and left it to the decision of the meeting as a whole. Here and on other occasions he, as is well known, displayed remarkable self-control; but as for the bishops, it will make a difference to them at the Last Judgement in what spirit they exercised the decision delegated to them.
Good point, William. He goes on:
When they expressed a preference for someone in clerical orders [i.e. not a monk], objections were raised: no cleric had ever been archbishop of Canterbury, save only Stigand, who had come into the see through impudence and had been properly expelled from it; there was no need for a custom of such long standing to be annulled, particularly as it could not be shown to conflict with the faith.
Disappointed in this plan, and being suspicious of the inflexible Faricius, the bishops made the following points in their deliberations: 'If that Lombard is made archbishop, there will be quarrels and schisms all over again. He will spare no one of us, especially as the king thinks as highly of him as if he had been sent down from heaven. [!] But this is not to be said openly. The argument we must use has to be one that wounds no one's feelings. Thus [they said publicly]: We have had more than enough foreign archbishops. There is good store of men who speak the language of the country, as learned as Lanfranc, as pious as Anselm, and monks like them both. There is, for instance Ralph bishop of Rochester, reputed the equal of the ancients, and better than both old and new for humility and approachability. If you trace his lineage, he is sprung from respectable Norman stock. If you enquire into his life, there is no blot on his copybook. He is the only one whose piety even malice could not carp at, for it is beyond cavil. If you look at his learning, he has drained all Athens dry, if you examine his eloquence, speech flows from his mouth like honey; and his language is that of his native Maine, meticulous and (so to say) well combed.'
Note that when they say they've had enough foreign archbishops, they don't mean they want an Englishman - it means 'a Norman, not an Italian'. None of the bishops at this council were English, and there wouldn't be an English-born Archbishop of Canterbury until Thomas Becket (of Norman ancestry, but born in London) half a century later. By 'the language of the country' they mean Norman French (and it's a bit surprising that Faricius, who was born in Tuscany but had been Abbot of Abingdon for nearly 15 years by this point, didn't speak it). The compromise candidate, Ralph, was Norman by birth but had been in England on and off since about 1102; he was appointed Bishop of Rochester in 1108 and was present at Anselm's deathbed. So he wasn't a foreigner by their standards.
You might wonder how William of Malmesbury knew what the bishops discussed behind closed doors, and how they decided what it would and would not be politic to say; the editors of the Gesta Pontificum suggest it's possible he got this information from his fellow historian Eadmer, who as a senior monk of Christ Church Canterbury was probably present at the discussions, and whom William had certainly met.
Anyway, the bishops' tactful realpolitik achieved their ends:
These opinions made the king change his mind and come round to their view forthwith. This took place four days after the fifth anniversary of the death of Anselm [i.e. 26 April 1114].
Let's hope it doesn't take that long to find a successor this time...
Quotations from William of Malmesbury, Gesta Pontificum Anglorum, ed. and trans. Michael Winterbottom and R. M. Thomson, Oxford Medieval Texts (Oxford: Clarendon Press, 2007), vol.1, pp.201-203.