Step 1 
Firstly you need to check your inspection chamber/manhole, you can easily prize the lid up with two flat headed screw drivers, if that is blocked then check your neighbours drains, if your neighbours drains are blocked see No 2 below, if not see No 3

Step 2
Check when your property was built, if 1937 or before, phone local water company, for confirmation of this, they will then advise you on whose responsibility it is to clear the blockage.

Step 3
If the drains are blocked solely on your property, then they will usually clear quite easily by drain rods, these can be purchased at your local D.I.Y. store, which is a cheaper option than a drain clearing company, if they will not clear, see step 4

Step 4
Your local council usually do have a drainage section, and the advantages of using them are, they are not a profit making company, which means you will get a honest and thorough job, they will have a set price for clearing the blockage no matter where the blockage is, where as a private drain company may have different prices for certain parts of the blockage.
If the council does not offer this service, they should be able to suggest a reliable company.

Step 5
You should be able to compare prices between, local authorities and, private drain company's.

Step 6
If property(s) are pre 1937 there is no need (if shared) to pay extra cover for drains, as they should be covered by local water companies regulations, unless your drains are blocked solely on your property.
If propertie(s) are post 1937, it would be a good idea to see sewer records (for free at council buildings) to establish weather insurance cover is worth extra money. 

Step 7
If you do use a private drain company, and they say your drains are in a bad state of repair, and need mending, ask them for proof of this, they should be able to supply you with this,by means of CCTV evidence, ( videoing your drains), but you must ask to watch the screen as they are performing this task, as some disreputable company's could be showing you a video of someone else's drains, if you have a good local authority they may also offer this service, which i would strongly recommend you use.

Step 8
Environmental Health Departments
If your drains are blocked and so are your neighbours, and you are on a private system, i,e built after 1937, or not covered by local water companies, they will be able to advise you who should be liable to share the cost of any drainage work that needs to be undertaken, this is free advise, just because your drains are blocked does not mean you are solely to pay for them, unless only your drains are blocked, then revert back to No3. ENVIROMENTAL HEALTH OFFICERS, have the power to serve legal notices on house holders who connect to defective drainage systems.

Step 9
If a private drain company advises you that a camera survey is required, this is not nessiceraly correct, a CCTV survey is usually advised if it is a repeated problem, if they block once every few years then you do not require a CCTV See note 7 about CCTV surveys.

Step 10
Home Insurance
Some home insurance companies may also offer CCTV service, dependant upon level of cover, some may charge for this service but it is worth a call to the insurance company to find out.