According to British English speaker and linguist F. R. Palmer, one can use
I haven't to go
or, in negation, preferably
I don't have to go
I haven't got to go
to deny that one has the obligation of going. Which means that the three sentences above can mean
It is not the case that I am obliged to go.
This is different to
I mustn't go
It is the case that I am obliged not to go (I must not-go)
Palmer offers the following as another example of haven't (got) to:
If you don't want to succeed, you haven't got (=don't have) to work hard.
If you don't want to succeed, it is not the case that you are obliged to work hard.
Compare this to
If you don't want to succeed, you mustn't work hard.
If you don't want to succeed, it is the case that you are obliged not to work hard.
However, Palmer states that haven't (got) to can be used like mustn't in the above examples of mustn't
You haven't got to play around in here
can mean either
It is not the case that you are obliged to play around in here
(Here haven't got to equals don't have to)
or "less commonly" (Palmer)
It is the case that you are obliged to not play around in here.
(Haven't got to equals mustn't).
See F. R. Palmer: The English Verb, 2nd Edition, sections 6.5, 6.6. Longman Linguistics Library.