Have to = Have got to We use them to express necessity in the present or the near future. However, 'have got to' is used especially in British English. 'I have to go to sleep now.' (= I've got to go to sleep now) 'Do you have to go?' (= Have you got to go?) They can also be used to give advice or recommend something: You have to try this recipe—it’s delicious.(= You’ve got to try this recipe—it’s delicious.)

I learn from learner again. In the US, "Have got to" is not preferred grammatically. I didn't know it was standard in the UK.

Both of them are correct and are equally common. In casual spoken speech, "have got to" is almost always shortened as in the following examples: I gotta / I've gotta go to the store. You gotta / You've gotta keep practicing. He's gotta sell his house. We gotta/ We've gotta wake up early. They gotta / They've gotta clean the house. Let me know if you have any more questions about this.