That's great to see Three UK now offer an unlimited cellular based data service. 😎
If you are using the Huawei E5573bs modem that they advertise on the Three website, I suggest upgrading it to the Huawei B525, which costs around £120. This has a much more sensitive antenna and provides better Wi-Fi coverage as well as 802.11ac, much like the router offerings of fixed line services. If the cell you're connected to is not heavily loaded, this could greatly increase the speed further, especially if it is or becomes 4G+ enabled.
Simple, to make sure you're getting what you pay for. This speed test is useful if you feel a connection slow down or want to see how your Internet is performing. This isn't like any other broadband speed test. TestMy's proprietary method is proven to help identify issues other speed tests fail to detect. The TMN Speed Test shows your true speed.