Here are some ideas of firms that would use class c (rigid) lorries :
Quarries/ Tipper haulage contractors
Demolition contractors
Builders merchants
Engineering/Pipeline merchants
Timber merchants/ wood pallet makers and dealers
Steel stockholders
Skip hire and waste disposal/recycling firms
Plant and tool hire firms
Tyre or car panel distributors
Car sales and auction yards with their own transporters
Scrap metal/recycling dealers
Overnight pallet network members
Furniture manufacturers/retail stores
Food manufacturers with their own lorries - (eg. google ‘Tiptree jam’)
Frozen food distributors
Food wholesalers and cash & carry warehouses
Brewery and soft drink distributors
Bread and cake bakeries
Produce (fruit & veg.) growers and wholesale merchants
Flower & plant nurseries
Dairies (both Milk tankers and bulk deliveries (trolleys) to shops)
Agricultural merchants/ Tractor sales and repairs
Animal feed merchants
*as for fuel tankers - eg. central heating oil home deliveries, I’ve always had the opinion that you should get a few years experience of ‘driving’ HGV’s (regarding the ‘feel’ of having a load on, cambering, defensive driving, etc. before being let loose with hazardous products on board. 
Good luck with your jobsearch. 