No it’s not normal , and there is no settling in period, so there are two possibilities for this apparent poor speed , first you have been mis provisioned by BT (basically your profile was set incorrectly to a lower speed , say 150 or 300Mb instead of 500Mb ) or the much more likely scenario, the way you are measuring speed is the issue or the device isn’t capable of using the new speed .
Measuring with WiFi devices isn’t necessarily a good idea to prove the speed being delivered , the underlying service can be fine but environmental issues affect the WiFi performance, that’s not within your ISP’s area of responsibility, and if using (for example) a wired device like a PC or laptop that’s not particularly upto date then it could be a limitation of the Ethernet cable or the Ethernet adapter in the PC that’s responsible for the poor speed test results.
How are you measuring the speed of your new FTTP service and with what device ?
