To start with, I'd look into British composers that were influenced by 19th century Orientalism, & may have been preoccupied with themes of Ancient Egypt, or any place in the Middle East where parts of the British Museum's collection came from. (I've not been there in decades, & can only vividly recall Champollion's Rosetta Stone...) Moreover, the choice of exotic music would also help to emphasize to the viewer watching that these ancient artifacts don't come from Henley-on-Thames or Bath.
In other words, I don't think the typical British pastoral scene depicted in English music makes any sense at all. So, the music of Vaughan Williams, Delius, & other British composers who have a strong connection to the English countryside are not the right choice. Though music inspired by the ancient Celtic world might work...
How about Sir Granville Bantock? He was drawn to both Oriental and Celtic themes in his music. Plus, such exotic music tends to be less boisterous and therefore might work well as background film music.
Below are links to a handful of Bantock's works, though I'll leave it up to you to listen to them, in order to decide if there's anything that you can use in your film. To my mind, Bantock makes a good choice because his music is difficult to place, yet it is British. Similiar to how the British Museum is quintessentially British, yet not at all British, considering its contents. Plus, Bantock is a neglected British composer, so his music can always use a good plug. (You might even sell some CDs for him or rather his legacy.)
--Serenade for String Orchestra "In the far West":
But it doesn't have to be a British composer. French composers were likewise strongly influenced by Orientalism: such as Charles Koechlin, for example, whose music tends to make excellent film music, anyway. Indeed I think parts of the following mysterious piece of music would work very well in a film or film documentary, & again, it's difficult music to quite place, though it certainly has a strong Middle eastern feel or inspiration behind it, at times,
--Les Heures Persanes, or The Persian Hours, which exists in versions for solo piano and orchestra. Here are two different recordings of the orchestral version (& I think that the Segerstam recording is the more evocative between them),
1. Orchestre Philharmonique de Rhénanie-Palatinat, conducted by Leif Segerstam,
Prt I: Charles Koechlin: Les Heures persanes (1913/1919) 1/3
Prt II: Charles Koechlin: Les Heures persanes (1913/1919) 2/3
Prt III: Charles Koechlin: Les Heures persanes (1913/1919) 1/3
2. Radio-Sinfonieorchester Stuttgart des SWR, conducted by Heinz Holliger:
Charles Koechlin - Les Heures Persanes for Orchestra, Op. 65-bis
Lastly, Koechlin's work, "The Seven Stars Symphony" might make good choice, too, despite that each segment is devoted to a different Hollywood icon from the golden age. So thematically it doesn't apply, but musically it might:
Charles Koechlin: The Seven Stars' Symphony (1933)
If you want any other suggestions of works by these composers, just ask, & if I can't come up with a recommendation, it's likely someone else here can.
Hope that helps.