Is the Concise Oxford Dictionary British English?
Solution 1:
The Concise Oxford English Dictionary gives word definitions and spellings in British English.
While I can find no explicit source for this, I infer this from the fact that Oxford University Press also publishes the Concise Oxford American Dictionary, which gives word definitions in American English, thereby implying the Concise OED gives the British English definitions*.
Furthermore, the OUP and by extension, the OED, is based in Oxford, England, which makes it highly likely the OED is a British English dictionary.
In summary, you are fine to keep using British English. If you are uncertain about whether a particular word or spelling you have used is British or American in origin, a quick Google search will probably put you on the right track.
*I would check this myself by looking up some words in it, but I only have the Collins English dictionary in my house. Somewhat ironically, I live 15 miles outside Oxford.
Solution 2:
English spelling should follow the Concise Oxford Dictionary
The Concise Oxford English Dictionary, was formally known as the Concise Oxford Dictionary:
The Concise Oxford English Dictionary (officially titled The Concise Oxford Dictionary until 2002, and widely abbreviated COD or COED) is probably the best-known of the 'smaller' Oxford dictionaries. The latest edition of the Concise Oxford English Dictionary contains over 240,000 entries and 1,728 pages (concise only compared to the OED at over 21,000 pages). Its 12th edition, published in 2011, is used by both the United Nations and NATO as the current authority for spellings in documents written in English for international use.
This dictionary is aimed at International English usage rather than British English, although:
In addition to providing information for general use, it documents local variations such as United States and United Kingdom usage."
Source Concise Oxford English Dictionary - Wikipedia
There is a separate Concise Oxford American Dictionary.