I am looking for the burial register of Arthur Henry Curtis who died on 25 December 1957 at Hampton House, Minsterworth.

Hi, welcome to the forum.
Despite searching the PRs I've not yet found this burial, altho there are a couple of other Curtis burials at Minsterworth before and after Arthur's so one hope's it is there somewhere.
That said, this site's database has many thousands of PRs, but only 3 Arthur Curtis, none in Minsterworth ?.

Is this your Arthur, from FreeBMD, Minsterworth is within Gloster Rural district so seems correct as far as I can tell, is the age correct ?

Deaths Dec 1957
CURTIS Arthur H 59 Gloucester R. 7b 577
http://www.freebmd.org.uk/cgi/search.pl

This age seems a possible fit for the following Marriage from this site's PRs, but for MINCHINHAMPTON, are you certain of the Minsterworth burial ?. (Minchinhampton is outside the Dean so no PRs in our database).

Marriage Details

Groom Surname Groom Forename Bride Surname Bride Forename District Parish Building Year Register Entry
CURTIS Arthur H YOUNG Elsie E Stroud Minchinhampton Holy Trinity 1921 C23/2 414

From GlosBMD http://ww3.gloucestershire.gov.uk/bmd/SimpleSearch.aspx

From FreeBMD again, I think this Birth fits the above Burial, also the Marriage confirms GlosBMD.

Births Jun 1898 (>99%)
Curtis Arthur Hayes Stroud 6a 324

Surname First name(s) Mother/Spouse/Age District Vol Page
Marriages Dec 1921 (>99%)
Curtis Arthur H Young Stroud 6a 795
Young Elsie _ Curtis Stroud 6a 795

HOWEVER FreeBMD also has this very similar Burial, which probably is a better fit(Stroud) for the above Birth & Marriage ?). So two very similar lives to untangle..

Deaths Dec 1961 (>99%)
CURTIS Arthur H 63 Stroud 7b 573

Ancestry suggests the Stroud man Arthur Hayes was born and resident in Nailsworth wrt 1901 Census, by 1911 the family are in Inchbrook, Stroud.

????

Any more info you can give to clarify your Arthur's life would be very helpful, thanks.

Arthur Curtis may have been cremated. Gloucester (Coney Hill) crematorium opened in 1953.