I agree with Peridot here, piano lesson will not help with 11+ state schools IMHO. Yes it might help in getting scholarship or just places in some good independent schools.
As far as that young age is concerned, I was also given the same advice about starting age and my boys started learning at Year 4 when they just turned 8. But I see in some music festivals some kids especially from a particular ethnic background playing high grades piano pieces at a very young age, which clearly tells me that they must have started at the age of 4 or even less. The boy who got the first prize for Level 5 piece was only 7. And I personally know someone whose son got fully funded scholarship place at Harrow School and that boy finished Grade 8 violin and piano by age of 11
But he is gifted child no doubt about it.
Coming back to starting early, yes I have also seen another friend (who himself is very musical, plays piano, saxophone, octapad etc) started piano lessons for his son when he is was 3yrs +, by age of 6 when his son did Grade 1, the little boy was bored and finally left it
A child will usually continue with some activity only if he/ she loves to do it otherwise gradually it becomes counter productive for both the DC and the parents.
If one is really keen , then can check with a music teacher whether the child is really gifted or talented and keen to do music at young age otherwise come back to it in few more years.