In Old English, /uw/ seems to have existed, but to have not been a very stable sequence, at least not in unstressed syllables. I'm not sure if it has the exact same distribution as /ij/.
I don't know very much about Old English so what follows is just based on quick research and may have errors.
A search for the sequence "uw" in the online version of the Bosworth-Toller Anglo-Saxon Dictionary turns up a number of results, including ones with "úw" (/uːw/). However, many of the words have spelling variants that may not include "uw". It's hard for me to say what this means.
For example, take widuwe "widow". The Oxford English Dictionary (OED) lists the following forms of this word as being attested in Old English:
OE widiua (Northumbrian), OE widua (Northumbrian), OE widuua (Northumbrian), OE widuw- (in derivatives), OE wydewa, OE wydywe (rare), OE–ME widewe, OE–ME widuwe, OE–ME widwe, OE–ME wydewe, OE–ME wydwe, OE (rare)–16 wydowe, lOE widewa
Wiktionary suggests that this word is reconstructed with the sequence *uw in Proto-Germanic (*widuwǭ), but I'm not sure what the basis for this reconstruction is. However, you can see related words in other Germanic languages on that page. Perhaps someone else who knows more will be able to address this point in another answer to this question; or if that doesn't happen, you can ask on the Linguistics SE site about the reasons for reconstructing a sequence *uw in Proto-Germanic.
Of course, in a standard accent of modern English, the related word ends in /oʊ/.
Likewise, Old English "caluw", listed in Bosworth-Toller as a variant form of calu, corresponds according to the OED to modern English "callow" with /oʊ/.
If it does turn out to be necessary, or at least preferable, to postulate unstressed /uw/ as a phonemic sequence of the language contemporary to "Old English" that was ancestral to present-day English (I don't know enough to be able to say how much evidence there is for this postulate), it would appear that it developed to modern English unstressed /oʊ/, spelled "ow".
Coda /w/ seems to have been uncommon in Old English
Original Proto-Germanic *j seems to have been lost in many cases when in word-final or word-internal position. The prevalence of coda /j/ in Old English seems to be mainly attributable to the vocalization of Proto-Germanic *g.
In contrast, Old English /w/ doesn't seem to have any common source aside from Proto-Germanic *w, so it seems to have been mostly restricted to the syllable onset.
Here is a relevant quotation I found in "The Vocalization of
Semivowels in Medieval English: A Quantitative Study," by Patrick Maiwald, 2017:
[w] occurred almost exclusively in onsets in OE [...]
Campbell (1977: 115) puts this difference [between w and j] poignantly when he writes that
“[t]heoretically w should never stand finally after a vowel in OE, for it was lost after some vowels, and combined with others into diphthongs […]. It was, however, often replaced by analogy [with inflected forms]”. In other words, lOE coda [w], i.e. [w] that was tautosyllabic with the preceding vowel, did exist, but only thanks to replacement processes after its general loss within the OE period, and not systematically.