The black population in Great Britain have no special accent, they speak English just the same as the rest of the population. But black people in America, for historical reasons, have their own dialect, sometimes called "Ebonics" in the past. They have many differences in vocabulary, grammar and pronunciation, though most black people today speak a variety of black English more or less similar to standard American English (except, perhaps, in pronunciation), and can easily switch to full standard accent if required. But part of the black population, especially in poor areas and low cultural levels, still speak a variety of their dialect so pure that the rest of the population may find it difficult to understand, not to mention foreigners.

This video link is an example of "soft black accent", the language is quite standard, only the pronunciation partly identifies this singer as a "black speaker": Forever.

And this other link is an example of "hard black accent". The accent is black, and so are the vocabulary and grammar (but curiously enough, the singer is a white man who was raised in a black neighbourhood): Informer.

Another black American dialect related to the continental one is the one spoken in the Caribbean area. The pronunciation of this variety is even closer to British English. You can see an example here: Pass the dutchie.

In pronunciation, their accent is basically American English but with some things which are closer to British English phonetics than to standard American. Here we are only going to talk about the most important differences.

THE LETTER R

The way black American people pronounce the R is basically the same as in BrE, that is, they only pronounce the R when it is followed by a vowel.

sorry BrE, Black English and rest of AmE /sɒrɪ/
teacher BrE & Black English /ti:tʃə/, standard AmE /ti:tʃər/

FINAL SCHWA / ə /

A final Schwa is pronounced very very weak in both BrE and AmE, but if it happens at the end of speech (if after the schwa we pause or stop), then in BrE it often opens and becomes a sound very similar to / ʌ /, but in AmE it doesn't change so often, especially because it is followed by /r/ most of the times..

teacher /ti:tʃər/ in BrE it sounds similar to /ti:tʃʌ / (but in the phonetic transcription we still use a / ə /
Black English usually does the same as British English, dropping the final  /r/ and opening the schwa.

THE CONSONANT -T-

In BrE this consonant sounds / t / in front of a vowel or between vowels. In American English it sounds / t / in front of a vowel, but it is flapped when it goes between vowels, like a quick / d / (we'll use the special symbol: / D / ) [it sounds like the Spanish or Italian flapped R, as in "cara"]

tourist /tɔ:rɪst/ /tɔ:rɪst/
Peter /pi:tə/ /pi:Dər/

But in colloquial BrE that also may happen. The difference is that the sound / D / occurs only in colloquial BrE, but in AmE that is the only possibility when the T goes between vowels (it is not optional, it's mandatory).

Some black people pronounce this intervocalic vowel like the British do, and some pronounce it like the rest of Americans do, that is, some say / t / and some say / D /. Besides, the authentic black / t / has no explosion, like that of BrE or AmE, so it sounds more similar to Spanish / t / than to English / t / (that is, more similar to English / d /).

PRONUNCIATION OF TH / ð /

/ ð / is usually pronounced / d / this /dɪs/

Black American English is not only a linguistic issue, it is also a social issue with its positive and negative implications. If you are interested in this topic you can watch this documentary, you'll learn about the language, its history and also the social implications.