After the free assessment, where a claim is accepted the solicitor writes to the other driver's insurer setting out the claim and the basis on which responsibility is alleged. The insurer investigates, usually by taking a statement from their policyholder, and then either admits responsibility, denies it, or makes a partial admission.
While that is happening, medical evidence is arranged. An independent expert examines you, reports on the injury and gives a prognosis. Where the injury has not yet settled, a further report may be obtained later so that the claim is valued on the injury as it actually is rather than as it first appeared.
The financial losses are then worked through and the claim is put to the insurer with a figure. Negotiation usually follows. If responsibility remains disputed, or the valuation cannot be agreed, court proceedings can be issued, which protects the claim and often brings the other side to a sensible position.