In theory yes, IF you only have handbaggage and you have boarding passes issued for each flight when you check in at Tallin. If you are flying with Ryanair, forget it! You will need to recheck in for your second flight when you arrive at Stansted, and you may have problems if your Tallin flight is delayed or if there is a long queue at Border Control to get landside. Even though you are an EU citizen with no baggage, if you are flying with Ryanair OR ANY POINT-TO-POINT airline, you will STILL need to enter the UK, and then queue to collect your second boarding card, UNLESS you have the possibility of computer check in before the flights.
Just a thought: ff your first flight is late in arriving, what would happen to your second leg?