Yup. Your challenge, should you choose to accept it, will be to have a nuclear Cold War between the British Empire and Russia (Russia's form of governement shall be left up to you)
Should you be able to kep South Africa, Canada, Ireland and Australia in the Empire, along with assorted island colonies, the Empire will probably have the necessary population base for this. India isn't a requirement, although the extra population would help the Brits immeasurably.