Jeans should NOT be worn for walking, as they are heavy and very cold when wet. Waterproofs - you will need a waterproof jacket with a hood and waterproof trousers. Gaiters may be useful for keeping your feet and legs dry although they aren't essential. Footwear - although trainers are adequate for mild summer walks, you will soon find you need something with more support. Walking boots are advisable and essential in winter or when taking part in more severe walks.
Leather walking boots are best, although there are some good fabric boots available.
Socks are obviously necessary - wool ones are best. Hat and Gloves - these are advisable in summer and essential in winter. Emergency food - it is necessary to carry items such as chocolate bars which you don't intend to eat except in an emergency. Whistle - this is in case of emergency when you will blow 6 quick loud blasts at 1 minute intervals. A reply of 3 blasts at 1 minute intervals implies you have been heard.