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Yes, they probably can. I prefer to let the medical expenses insurers make their own claim directly off the insurers, because of the risk of the case going wrong after you get an offer settling global sums, which your solicitor advises you to accept.
The real problem comes when your solicitor has said that your claim is worth £20,000, and there’s an offer of £16,000. There are areas of your claim which are quite weak, and you should take the £16,000. But if £5,000 of that claim relates to medical expenses, you’ll have to pay the whole £5,000.
You should ask your solicitor to get confirmation from your medical expenses insurers that he will do his best to recover their outlay, but whatever he recovers, they’ll have to be satisfied with and can’t come after you for more.