No offence but no one is going to investigate you for transferring just £40k.
Most banks will let you transfer £10k a day using the fast payment system online no questions asked, so you could easily transfer the whole amount in 4 days via the phone App. If you wanted to transfer the whole amount in one goal just do an old fashioned bank transfer - but you will have to pay a fee for this.....
Employing a solicitor to oversee the transfer of £40k is mad, they will happily do it am sure and walk away with a £ks for the service
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You are seriously over thinking this if its the transfer bit you are worried about. £40k might be alot of money to you, but to the banks it's pocket change and as such doesn’t warrant any increased security.