We can't give you a specific time frame, but non urgent referrals can take between 4 to 6 weeks, sometimes longer, and this will vary a little in different regions.
There is information about what happens at a breast clinic appointment on the link,
The majority of referrals to a breast clinic, turn out not to be cancer, and can be due to a number of benign (non cancer) breast conditions. But it is sensible to get checked out at a clinic anyway.
