No need to throw bedding/ clothes out, just put in a dryer (at 60 degrees) for 30 mins then seal in plastic till after treatment which can be chemical, heat or freeze, see below from 'NHS Choices'. Unfortunately the council have a waiting list but can give advice so if you choose a private contractor make sure they are registered (see below).
"Bedbugs can be very difficult to get rid of. Your best chance of successfully treating an infestation is to get professional help.
Contact your local council or a pest control firm that's a member of the British Pest Control Association or National Pest Technicians Association.
A technician will carry out an inspection to confirm an infestation. They can then use special treatments such as insecticide, a steamer or rapid freeze system to get rid of the bugs.
They may also advise about things you can do to help, such as:
wash infested clothes or bed linen at 60C, or put them in a dryer on a hot setting for 30 minutes
use a vacuum cleaner with a hose to suck up any bugs you can see – dispose of the contents of the vacuum cleaner in a sealed bag
consider throwing away any mattress or furniture that's heavily infested
use plastic mattress covers that encase the entire mattress – this will stop any bedbugs getting in or out"
For an eco option you could try www.eco-friendlypestcontrol.co.uk - My friend had BB's but not sure who he used but he did use an eco company. So sorry to hear you have them!!