According to British R.P. there are 20 vowels and 24 consonants in English.
Vowels are classified according to the part of the tongue raised and the height to which it is raised. They are divided into pure vowels or monophthongs and vowel glides or diphthongs.
Pure vowels are further divided into three parts according to the part of the tongue raised. They are classified as front, central and back vowels.
Front vowels : There are four front vowels.
The first front vowel is a long sound as we have in the words eat(initial sound), beat(medial), and tea(final).
The second is a short vowel as we have in the words it, bit and city(final).
The third one is as we have in the words ate and bet. This vowel sound does not occur word-finally.
The last one is as we have in the words like add and mad. This vowel sound does not occur word finally.
Central vowels : There are three central vowels.
The first central vowel is as we have in the words up and cup. This vowel sound does not occur word-finally.
The second is as we have in the words earn, learn and blur.
The third one is called schwa . It is a weak vowel e. g. above(initial), decorative(4th and 6th sound) and mother(final).
Back vowels : There are five back vowels.
1 In the words like art, heart and far.
2 In the words like odd and hot. This vowel sound does not occur word-finally.
3 In the words like all, call and law.
4 In the words like book, wool and sugar. This vowel sound does not occur word-initially and finally.
5 In the words like ooze, booze and zoo.
Thus there are 12 pure vowels.
There are eight diphthongs. Diphthongs carry two vowel sounds in which the first vowel sound glides towards the second. That’s why they are called vowel glides. They are further divided into three parts.
Vowel glide toward /i/ There are three diphthongs in this category.
1 In the words like aim, name, ray.
2 Words like idea(initial), bite, cry.
3 Words like oil, boil, boy.
Vowel glide toward /u/ There are two diphthongs in this category.
1 In the words like ocean, home, go.
2 In the words like out, bout, now.
Vowel glide toward schwa There are three diphthongs in this category.
1 In the words like ear-ring, theory, cheer.
2 Words like aerial, Mary, fair.
3 Words like during(medial) and tour(final). This diphthong does not occur word-initially.
Thus there are (4+3+5)+(3+2+3)=20 vowels
There are 24 consonants. I’m giving the list according to the place of articulation.
Bilabial : Lower lip against the upper lip. There are four consonant sounds in this category.
/p/ as in pen, support, map
/b/ as in boy, obey, rub
/m/ as in man, commit, farm
/w/ as in wine and quality. It does not occur word-finally.
Labio-dental : Lower lip against the upper teeth. There are two labio-dental consonants.
/f/ as in fan, offer, roof
/v/ as in van, nephew, give
Dental : Tip of the tongue against the upper teeth. There are two dental sounds.
th as in think, ethics, bath
th as in this, leather, bathe
Alveolar : Blade of the tongue against the alveolar ridge. There are six alveolar sounds.
/t/ as in ten, cattle, bat
/d/ as in den, sudden, bed
/s/ as in sip, icy, bus
/z/ as in zip, resolve, buzz
/n/ as in nun, annul, ban
/l/ as in lip, below, bill
Post-alveolar : Tip of the tongue against the back of teeth ridge. There is only one post-alveolar sound.
/r/ as in red and very. It does not occur word-finally.
Palato-alveolar : Blade of the tongue against teeth-ridge and simultaneously front of the tongue against hard palate. There are four palato alveolar sounds.
ch as in church, birches, bunch
j as in jug, g as in agenda, g as in huge
sh as in shin, gushing, brush
s as in measure, g as in rouge
Palatal : Front of the tongue against the hard palate. There is only one palatal sound.
y as in yes. As in university(first sound) and as in student(3rd sound)
Velar : Back of the tongue against the soft-palate. There are three velar sounds.
/k/ as in cat, rocket, back
/g/ as in gun, begin, bug
ng as in singer(medial), sing(final). This sound does not occur word-initially.
Glottal : From the glottis. There is only one glottal sound.
/h/ as in head, behead. It does not occur word-finally.
Thus there are (4+2+2+6+1+4+1+3+1)= 24 consonant sounds in English