England and Wales
In addition to a permit to fish, any angler aged 13 years or over, fishing for salmon, sea trout, trout, freshwater fish or eels in England (except the River Tweed), Wales or the Border Esk and its tributaries in Scotland must have an Environment Agency rod licence. A licence can be bought online here or by calling the EA. Licences are free for 13-16 year olds, a fee is payable for those over 16 years which varies by species and duration.
Money from the sale of licences helps to fund work managing rivers and lakes. If you are caught fishing without one, you could be fined up to £2,500.
Scotland
There is no requirement in Scotland to have a licence to fish, however an angler must have the legal right or permission to fish. There is no salmon or sea trout fishing on Sundays anywhere in Scotland (except the Border Esk in Dumfriesshire which is dealt with under English law, since much of the river is in England).
Rules on catch & release are tightening all across the UK and Ireland. In Scotland many rivers now insist that all salmon are released. Please check local rules before fishing. All fish whether dead or alive must be returned to the water. Some rivers have local later dates, for more details go to Scottish Government website