Thames Water cancelled account without my permission and now I have a £500+ bill

Brie

See if there's a special needs/vulnerable customer team that you can talk to.  They're the ones that set up arranged payments for those that have different water needs such as you seem to have had in the past. 

I suspect that with the account having been cancelled your special arrangement has also been cancelled and someone may have recalculated as if yours was a standard household.  if your child requires a high volume of water for frequent bathing for instance this might justify the much higher than usual amount being charged.  That might explain the situation but it doesn't make it right.  

Hopefully they will come to their senses and sort things out in your favour.