I went through a breast cancer scare this summer. Fortunately, the final result came out as fibroadenoma and not cancer, but I can now understand the fear that people experience when they first find a lump.
As a result of my own experience, what I would highly recommend is that if you cannot wait out the two-week NHS appointment, DO keep that appointment and attend it, but that you can also consider getting a same-day/next-day ultrasound scan at a private clinic (but do make sure it’s a verified clinic with properly qualified specialists). I paid 350 pounds to go to a clinic in London two days after I found my lump, and for me, it was worth doing, as I instantly had a very good idea of whether my lump was likely to be cancer or not. The result from the ultrasound was already highly indicative of fibroadenoma, which brought my anxiety levels right down. Even if the result turns out to be indicative of negative news, it means you have up to a two-week lead to research and make some decisions ahead of your NHS appointment. If nothing else, the private appointment gives you a form of a “second opinion” which can end up becoming useful in itself (in my case, it allowed me to buy some time to decide on getting a biopsy because I have a needle phobia).
The private clinic offered a very extensive ultrasound scan. In fact, it turned out to be a much more thorough exam than the one I then got via the NHS, including the fact that my private scan picked up a total of five masses (two of them cysts), whereas the NHS mammogram and ultrasound only picked up one mass (somewhat worrying). I also got a very thorough hands-on physical inspection and learned the correct way to conduct a self-exam. (In contrast, the NHS consultant did a very light tap of my mass region only.) The person who examined me at the private clinic was one of the leading people in radio-imaging and breast cancer, and I got a lot of useful advice from her. I felt very reassured by her information.
Sadly, I can understand that not everyone is in a position to afford to get a private appointment, but if you can do so, I believe there is no better thing to spend your money on than on your health.
A point of caution: An ultrasound by itself can reveal a lot, although it cannot pick up on calcification (which a mammogram does), so you cannot take ultrasound results as 100% conclusive, and is why it remains important to follow through with your NHS appointment.