It is not a good idea to travel with a large sum of cash but you'd get te best rate if you could find a trusted expat who wants to change their euro salary into pounds. Next best might be if you could pay for something with a credit or debit card (different cards have different fees though). Next best might be to use a currency specialist but this option comes with the risks of doing business with a company that you are not familiar with.
If none of these options are practical then yes, a telegraphic transfer between two banks accounts should be the next choice. You will need to visit your branch, fill in forms and show ID. You will be charged about £20 and the rate will be reasonable.