I don't know how formal an arrangement your wife had with the well off lady. If she was an employee, then the well off lady should have been operating PAYE and subjecting your wife's pay to tax and national insurance contributions assuming that her total income made her liable to tax and NIC. Your wife may have worked for her on a self-employed basis so that she was responsible for her own tax and NIC.
Financial inducements to accept a job are taxable. However, they aren't usually paid and taxed until the employee starts the job and it's not clear that you did that. Yours was a far less formal arrangement than would be the case where a big company takes on a new employee and pays a signing on bonus. Given that your wife was the lady's carer and you may have actually given up your job to be on standby, so to speak, when your wife wasn't available, there is circumstantial evidence to suggest that there is a connection between the gift and your actions and HMRC may take an interest if they get wind of the situation. That evidence will be strengthened if you did act as the lady's carer during the period from June 2012 to the time that she passed away.
It seems to me that the family as opposed to the solicitor may be trying to find out the reasons for the payment with a view to trying to claim it back from you and you may have to consult your own solicitor. If you are honest about it, then you could be landed with a tax liability though the tax and NIC should strictly have been dealt with by the well off lady.
Even if you said the cash sums were gifts, their value will need to be included in the valuation of the well off lady's estate for Inheritance Tax purposes as she died within seven years of making them. It could also be argued that they were gifts with reservation of benefit as they weren't made without conditions attached.
If the well off lady's estate does not have the cash or assets to settle the IHT you could find yourself having to pay 40% Inheritance Tax. Take a look under the heading "When a beneficiary or a 'donee' has to pay Inheritance Tax" here
. Given that you say she was well off, I'd be surprised if there is going to be a problem for the estate in paying any IHT liability.
I'm afraid that there is no straightforward answer here. You really need to try to find out what the well off lady's family's motives are once you have told the solicitor what the payment was for, wait to see what happens after that and be prepared to consult a solicitor if the need arises. HMRC may well be happy to get the 40% Inheritance Tax on the sums paid to you from the estate as opposed to you in the form of IHT or income tax and NIC, though I have to say again that my own view is that you were effectively paid a sign up bonus and that makes it liable to income tax and NIC.
I realise none of this is great news for you. Let me know if you have any further questions.