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Upon checking the supported frequency bands of Lumia 810 (RM-878), the phone supports the frequency bands being used in the UK. Here's the frequency bands supported by the phone and being used in the UK:
GSM 900, GSM 1800 mHz
UMTS 900, UMTS 2100 mHz
GSM 850 900 1800 1900 mHz
WCDMA HSPA+ 850 1700 1900 2100 mHz
To confirm the functionality of the phone within the UK, you still need to check with the operator if they use or support the frequency band of the phone.