Hmm this is a real problem. The thing is she wasn't insured, and it's, as unjustified as it sounds, treated as 100% her fault as she hit the back of the van.
Now if this older women is prepared to lie as she sees this an an opportunity to get money, and I strongly suggest she is, she will know to lie about the pain in her neck and/or back and not elsewhere. The reason for this is that medically they are the 2 places left for which doctors can't PROVE she's lying. They do not know the level of discomfort. Basically if she says she's got a broken arm a doctor can say 'that is definately a lie'. If she says her neck is aching constantly a doctor can only say 'We do not have the technology to determine if she is lying or not'.
It's not coincedence people always say they've hurt their neck or their back.
Now £7000 is probably a reasonable amount for a consultancy, specialists etc to see her about her neck. Especially if she is going for 'constant pain' and 'lack of mobility' which generally gets the most wonga. In fact £7000 is a relatively small amount of money for such injuries. Remember no doctor has the capability to prove she's lying, so all she has to do is say 'I am in constant pain I can't stand it will it never end' and no doctor is going to stand up and say 'I believe that is a lie'. Horrible really.
The good news however is the fact that they have put such a tight deadline on giving the money makes me think they are probably after a 'quick-win'. They don't REALLY want it to go to court - they want you just to panic and pay up or make an offer. If you DO pay up (after offering them £2000, £3000 or something first of course), make sure you have something signed saying this is in total and final payment including costs - otherwise in 18 months they could (and will) come back for more.
They probably know you were uninsured. They also know
1) Most people are scared to go to court and think it's somehow bad.
2) Court costs most people money especially if they lose.
See if your brother can get legal aid. If so, I'm afraid you're best bet is going to court. This is NO-WHERE NEAR AS BAD AS IT SOUNDS. Just make absolutely sure you don't lie in court otherwise you'll get ripped to peices.
It's a real problem that the driver was uninsured, a serious problem, however this is not really material to the court case. It just means NOW if your brother has some money he's going to have to pay for his own defence. It is irrelevent with regards to how much old-women will get. Remember, with injuries, the suggested rate is only £20,000 for the loss of an eye - everything else is lower.
If you do go to court and lose, of course you have to pay out of your pocket THEIR court costs as well as your own. This could unfortunately be up to 25K or something as their lawyers will be charging out at £100 - £200 per hour. You can potentially NOW get insured against losing the case (!!), which would be worth looking into.
For a quick win I'd phone and offer then £1200 in full and final settlement and see if they bite (probably not). Tell them when you do this it should not be considered an admission of guilt.
Good luck. Don't drive uninsured kids! By the way - find out what the 'statute of limitations' is for the crime she committed. May well be less than 2 years at which point BINGO! You win!