If you are at a crossroads and you face another car on the other side of the road, and if you are both turning right, neither of you have priority.
If you face another car at a crossroads and that car facing you is signalling and intending to turn left, generally that other car has priority to turn left.
If you are on a major road waiting to turn right onto a minor road (you are waiting in the centre of the road signalling), and an oncoming car coming toward you is signalling left to turn into the minor road (where you intend to turn) That car signalling left has priority.
If in doubt never assume you have priority, always make sure you absolutely know the intention of the other driver. Never ever assume they are turning left just because they have a left hand signal on, because sooner or later one will go straight ahead.
The official DVSA guide to Driving - the essential skills