Pay attention to the three pillars of oral posture:
First of all, let us consider the default anatomical position of the jaw. In RP, the jaw is often raised up and this reflects the poshness and social status of those who practise RP. So, if possible, try to keep your head up, expose your neck and demonstrate you are scared of absolutely nothing.
Next, think about the lips. Pay attention to my lips when I say: “Sure”. I will say it twice. First, with an American accent, the second with a British accent. Pay attention to my lip corners. Are they stretched apart or do they move forward? /ʃɔːr/ Clearly, the lip corners stretched back in an American accent. /ʃʊr/ Here, the lip corners move forward and close together . So, to maintain a RP British accent, be aware of keeping your lips together and not showing so much teeth, as opposed to Americans.
Lastly, the tongue. Is it in the front or the back of the mouth? Close your eyes and say Roger lost his dog with an American accent. Now say it with an RP accent. Do you feel the tongue position changes from the center of the mouth to the front of the mouth?
Here is another classic example in RP when the tongue is in front of the mouth: /ʃʊr/ as opposed to /ʃɔːr/ where the tongue is rolled back in American English.