Driving relay with ESP8266
There is no reason to combine LED and Q1 control in one net. With your overly inventive schema you only push the functionality into a corner, since the LED might have a bigger forward voltage, and the transistor might need extra push to provide a necessary current for the relay, and GPIO might deliver only 2.7-2.8 V under load. Also you have no independent control of LED brightness, 5-6mA might be too much for modern LEDs as logic indicators, too bright. 

Just put a series resistor from GPIO to the base of your transistor Q1, and put your LED in parallel to that GPIO, with another limiting resistor.