By the regs, the breaker protects the in-wall wiring, so your 20A breaker and 2.5mm wire will be totally fine for a constant load of 20A.
The charger will only draw 16A max (in reality they often draw a bit less. Mine draws 14.5 from memory) so you've still got 4A you can pull from any of those other sockets.
You're likely to charge overnight, so perhaps those other loads won't even be on at that time? And during the day your charger isn't on so you can pull all 20A out of those other sockets.
In summary, you should be fine by the sounds of it. Again, the sparky can confirm that.