Matron Can't Grow Carrots!

I live in hope... that one day when I pull at that perfectly round top, that there will be a perfectly straight carrot under the soil!Here in London the soil is typically London clay. Great for some veggies, but generally not so good for root veggies. I do add extra sand to the soil when I am trying to grow carrots, but perhaps I need more?
Of course these would be rejected by a commercial supermarket, but that is their loss. I cleaned and grated these carrots within 10 minutes of picking. The scent and flavour of fresh picked carrots is amazing. Grated carrot in a plain balsamic vinegar dressing. Who could ask for more. Wonderful!