Robusto is right. It's simply a d with a y-glide because the u is pronounced as a u and combined with the sound of the letter before it (d). It’s the same with multiple, other words. Like music or enthuse.
It’s a nuance in the British way of speaking English that seems to be lost on certain people. That's why it is sometimes mispronounced and the u gets merged with the previous letter to form a different sound. The example given in the question, the word duke, will end up sounding like djuke when mispronounced by people who fail to appreciate the nuance of the u.
When pronounced properly, duke will not sound like djuke. As Robusto wrote, it should sound like dyook.
This is because the letter u should be pronounced as a u; rhyming with the word you. When pronounced, the letter before it should be combined with the u but, not merged with it. In this example, pronounce the d sound and then the u, without a pause. It's like the words do and you. When in the same sentence, they would be pronounced separately. Now imagine that there is no gap between them so that they are written doyou. Now imagine that the o after the d were removed. That would be written as dyou. Then add the k sound on the end. Therefore, dyook. That's the way to pronounce duke correctly.
You can apply the same method when pronouncing other words, that are like that. For example, enthuse. Consider the th sound and then the u.
What’s strange is why this has generally been changed in American English to an oo sound. I say generally because this does not seem to be the case with the word music in American English. I haven't noticed any Americans say moosic.
Another thing worth mentioning is that this is not particular “Received Pronunciation”. It is common across the UK, eve for people with different regional accents.