Is your claim for personal injury or was it a damage only?
If you were injured, there are a number of things to consider.
Firstlly, the other side will often make what is called a part 36 offer at a reduced value in the hope that if accepted they will get away with paying out a lower amount.
However, your solicitor is the only person who can advise whether the offer is acceptable as he will have all the facts, your medical history and all the relevamt details in front of him and will therefore have a reasonably good idea in his own mind the sort of value that would be deemed acceptable.
If your solicitor thinks it is an unreasonable offer, then he/she can make their own part 36 counter offer.
If an agreement cannot be reached by the time the 3 years statute of limitation arrives, then your solicitor will then issue proceedings with a view to a Judge deciding, but it is usually once proceedings have been issued that the third party starts talking seriously, as they know that if the case proceeds to trial, then they will become liable for all the court costs as well, which can be substantial.
Your solicitor will advise you as to whether he feels the offer should be rejected or accepted, but he/she cannot accept or reject without first consulting and advising you, that has to be your decision.
Yoour solicitor will have drawn up a schedule of damages, both special damages and general damages. General damages covers your actual injuries and includes a value for pain and suffering, whilst special damages covers all your other expenses, for example damaged kit, loss of earnings etc.
So ask your solicitor how the offer compares with his schedule of damages.
If it is a damage only claim, in most cases the third party insurers will offer trade prices. The courts ruled some time ago that a claimant should be returned to their pre crash financial position and as not that many people have access to purchasing bikes or cars at trade prices, the value offered should be for a like for like vehicle at retail prices. Clearly if you are offered trade values, then you will have to put money to the purchase to get you back to where you were, and so you end up being out of pocket, the courts have deemed this unacceptable, the insurance companies know this, but they will still try it on and try and save themselves a big wedge of cash because it has not been that well publicised.
So speak to your solicitor, (if it is an injury claim) although to be honest if you were injured and the offer has come via your solicitor, then they should have advised you anyway.