tl; dr: We don't have much reliable evidence on Harald Fairhair (Hårfagre), let alone his alleged "diplomatic" relationship with the British Isles.
I summarized what we can say about the historicity of Harald and his son, Håkon the Good (den gode), with relative ease before in the following question threads:
I also introduces some basic premises on the primary sources on the 10th century northern British Isles/ England in: Are there any good Anglo-Saxon sources that speak positively about Viking, Viking culture, or Viking Society?
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Then, I assume OP would like to know more about the surrounding of the alleged upbringing of Håkon, son of Harald, at the court of King Athelstan of England (r. 924-39), mainly from the British point of view (that is to say, sources). While the majority of scholars tend to accept the historicity of this tradition "to some extent", we unfortunately don't have enough evidence either to confirm or to refute the account of later traditions from the late 12th and 13th centuries, such as Heimskringla.
In addition to the dearth of Anglo-Saxon/ British contemporary texts, the most fundamental problem is the identification of the historical person appeared allegedly both in Scandinavian texts and in British texts, almost solely based on the name.
A later Anglo-Norman text, William of Malmesbury (1120s), certainly narrates the visit of two envoys (Helgrim & Osfrid) from a certain Harald, "king of the Norwegians (rex Noricorum)" in York under the rule of Athelstan (927x939). While the date seems to corresponds well with the latest days of Harald Fairhair (his death is now customarily dated to 932/33 CE), we don't have any conclusive evidence that determine whether this "Harald (Haroldus)" really was Harald Fairhair - the name of envoy mentioned in the saga is at least different from those of them. This is also the only British (including Anglo-Saxon) source that narrate the possible diplomatic relationship between the Anglo-Saxon and Scandinavian (in a geographical sense) rulers in the early 10th century, in spite of the huge gap (about 2 century) between the alleged event and the date of the primary texts.
Nevertheless, the current academic consensus seems to regard Harald's alleged relationship with Wessex-England, represented by his son's upbringing narrated in the saga, as "historically/ situational possible", rather than either to confirm or to refute the entire possibility (as for more details, please see my second post).
OP perhaps also would like to refer to another possible connection between Harald (or Harald's another son) and England - namely Eric Bloodaxe (Eirik Blodøxs), however. It is true that "Eric", as the king of Norway and/or as the king of York appear both in contemporary Anglo-Saxon sources and in later Scandinavian tradition, but some scholars (Peter Sawyer & Clare Downham) have recently disputed this long-established identification: That is to say, Eric, Viking King of York, was not the same person as Eirik Blodøxs (that is to say, there were two different Eiríkr around the middle of the 10th century) (Sawyer 1995; Downham 2007: 115-20)! On the other hand, other scholars like Williams and Woolf still defend this identification (Cf. Williams 2010: 79-96).
Except for the shared name (Eiríkr), however, our most direct evidence on the identification is also not flawless - the skaldic poems by Egill Skallagrímsson in his saga (Egil's Saga), written in the early 13th century. Egil's saga belongs to the sub-category of "the saga of Icelanders" (also called as "Family sagas") within Icelandic sagas, and the historical authenticity of the texts (as well as the verses incorporated in the prose texts) under this subcategory of sagas are generally not so highly regarded than royal biographies (kings' sagas). So, as is similar with the case of his brother, Håkon's upbringings, it is difficult either to confirm or to refute this famous episode of exile and death of Eric as well as its possible prehistory during the reign of Harald Fairhair, based on the current extant primary sources.
References:
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