What is the country code and area code for Plymouth UK?

The code within the UK is 01752. In international format, that's +44 1752.

(The plus sign means "insert your international access prefix here." From a GSM mobile phone, you can enter the number in full international format, starting with the plus sign. The most common prefix is 00, but North America (USA, Canada, etc.) uses 011, Japan uses 010, Australia uses 0011, and many other countries use different prefixes.)