In a regular situation, the stamp duty on a purchase of a £300,000 residential property would be £5,000 (£125,000 x 0% + £125,000 x 2% + £50,000 x 5%). See the calculator here
On the face of it, you are selling your home to your children for £300,000 with the new mortgage paying off the old one. As your children will be legally responsible for the mortgage payments, notwithstanding the fact that you are paying it, a transfer of value has occurred (legal responsibility for the mortgage) and that gives rise to a stamp duty liability. The property will also be transferred from you to your children.
What concerns me is the phrase "for my benefit". Are you giving up ownership of the property forever? If not, your solicitor may be able to argue that there is no sale and no stamp duty. If your children will retain ownership benefits, then there is a sale and stamp duty arises. I would have expected the solicitor to have an idea of the stamp duty position and ways around it, if any. My own view is that stamp duty of £5,000 will be payable.
I hope this helps but let me know if you have any further questions.