The pronunciation of consonants is practically the same in American and British English with two big exceptions:
THE LETTER - R -
In BrE they only pronounce the R when it is followed by a vowel. In American English the R is pronounced in all positions.
teacher /ti:tʃə/ /ti:tʃər/
park /pɑ:k/ /pɑrk/
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"]
Peter /pi:tə/ /pi:Dər/
But in colloquial BrE that also happens. 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).
You can find lots of examples of this change in the following song: Stitches.
See Pronunciations of T for more information.
Now, here are all the English consonants, symbol and pronunciation. Watch the video and repeat.
And here is a teacher giving some explanations
The Phonetic Chart (vowels and consonants)
To see the different pronunciations of T and R in action go to this phonetic lesson based on the pronunciation of the British band One Direction: Phonetics with One Direction - Story of My Life