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Kopkid64 The third party insurers are simply deploying delaying tactics as it is their way of slowing the claims process up as they use the excuse that they are carrying out their own investigation, so nothing unusual in that respect.
The statement of truth is nothing more than your statement of events, but unlike when you make a statement to the Police, this statement is under different rules called Civil Procedure Rules (CPR) and is used in a civil court. Unlike a statement you make to the Police however, you are allowed (within reason) to say whatever you like which includes opinion and hearsay which you are not allowed by and large to use in a Police statement.
This statement can then be used in court as your evidence if it gets that far, and chances are your witness will also have been asked to make a similar statement.
So all I can say is make your statement, keep it as accurate and truthful as you can remember. If I was taking your statement, it would still be called a statement of truth, so that is all it is, nothing to be worried about.
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NMNeil as far as getting a copy of the Police report and statements, this can only be obtained by paying a fee (usually around £85) and statements will not have been taken for a damage only crash as the Police do not deal with them by and large these days, but even if statements had been obtained, being section 9 statements (Magistrates Courts Act) these are not released until a case is closed and even then only certified extracts, which also applies for any crash reports (only certain parts are released).
So little point in contacting the Police because no information will be forthcoming (assuming they have paperwork on the matter in the first place) unless an approach is made m-by an appropriate body such as a Lawyer or crash management firm, the appropriate fee is paid and is not an individual.