It is a common misconception, partly because of bad use of terminology, that the English 's construction is closely equivalent to a genitive in languages like Latin, German etc with overt case marking.
But in reality, 's works quite differently: it can be appended to the whole noun phrase, including adjuncts such as prepositional phrases and relative clauses. This means that the following are in principle perfectly common and grammatical:
(a) [The girl next door]'s dog just died.
(b) [That man I saw yesterday]'s car is parked in my space.
(c) [The queen of England]'s crown is worth its weight in gold.
Of course, if you find that having a lengthy or syntactically complex noun phrase is clumsy to read, you can always rephrase. In reality, a case such as (b), though fairly common in spontaneous usage, would probably be avoided by careful writers. But a phrase such as "The queen of England" is short and simple enough that there's no need to contort the sentence in my opinion.
To avoid confusion, I personally avoid applying the term "genitive" to this construction in English. That way you avoid false expectations if you're used to the more prototypical "genitive" of other languages.