Most wanting a delay are Labour-led but two are Tory councils and one is a Lib Dem authority.
Health Secretary Wes Streeting says Craig Guildford has put "a stain on his character".
Nurses union says long waits and corridor care having a devastating impact on paitents.
Anger is high after thousands of customers in Kent and Sussex have experienced days of water chaos.
The former Conservative minister and Scottish Tory treasurer has been officially unveiled by Nigel Farage.