Well... In your dashbord, select Woocommerce -> Settings
Select the Shipping tab
At the top you should see links with all available options
Fill the infos for the flat rate option (£6.95).
Check the box to activate it.
Enter a title for this shipping option (this is what your customers will see)
Enter the shipping rate (£6.95)
Then, select if this shipping option is available for all the countries or specific ones.
Select: by order for the next option
And select if it is taxable or not.
Fill the other options if you need them...
Than fill the infos for the free shipping option (over £300).
Check the box to activate it.
Enter a title for this option.
Enter the minimum amount required to get the free shipping (£300)
Leave the box uncheck for the needed promo code, as your customers won't need a promo code to get it free.
Finally, select if the method is available for all countries or specific ones.
Hope it helps!