Amitoria, I can assure you that these two words are NOT pronounced the same way in British English, or in any other variety of English.
Think about it logically.
Do you think it is likely that an everyday modal verb like 'can't', which we all say a dozen times a day, would really have an identical pronunciation to the most vulgar and offensive taboo word in the language? Of course it isn't!
In BBC English, RP English, or the 'standard' pronunciation you hear if you click the GB audio button on any online dictionary, the word 'can't' is pronounced with a long 'a' sound. It begins the same as the RP pronunciation of 'car'. It's a long vowel sound made with the tongue in a very low position. If you say 'caah', with a long 'a' sound, then add 'nt', you'll get the standard GB pronunciation of 'can't'.
The other word rhymes with 'hunt' or 'runt'. This vowel /ʌ/ is a short sound, pronounced with the tongue in a mid-position. There is no chance of confusing this with 'can't'.