It's easier to use the comparison sites. Just make an estimate of current bills. If you are not sure make 2 or 3 estimates- maybe higher and lower end of the likely range- and see if you get the same cheapest supplier each time.
It would be good if we could compare unit charges but they deliberately make it too complicated with standing charge/no standing charge options, higher rate for first X units then lower rate for the balance, economy 7 , dual fuel discount, DD discount, paperless billing discounts etc. And some give a discount/rebate at the end of a set period- often 12 months. It's just too messy