You don't need any equipment to enjoy nature, though good footware and warm, waterproof clothes can help! But to identify more than the large and obvious species then some simple equipment aids are of real benefit.
Books and keys
Details of both online and printed guides and described on the relevant wildlife group ID pages. If you can recommend any other sources then do let us know.
There is a huge range of binoculars on offer, to fit various budgets. Look for one that does close-focussing (2 meters or less) so you can use them to look at insects such as butterflies and dragonflies. Binoculars commonly have a spec such as 8x32 or 10x42. The first number refers to the magnification (eg. 8 times or 10 times) and the second to the diameter of the objective lens. Whilst x10 magnification sounds better, the downside is that you see a narrower field of view which can make it harder to scan larger areas or find your subject. Larger objective lenses gather more light but the downside here is that they have more glass so weigh more. Ultimately it comes down to personal choice.
A camera is essential equipment for recording, both to help you identify what you've seen but also to attach to your record as evidence. As most UK wildlife is small, a camera with a good macro function is really helpful. Mobile phones are fine for plants and larger species but less effective for anything small and especially if it flies. However many small and cheap compact cameras have excellent macro abilities, and also have the benefit of easily fitting in your pocket, so you don't have to spend very much.
Higher quality images generally require a better camera (though the photographer is the most important factor!). Serious wildlife recorders and photographers will usually invest in either an SLR or a bridge camera. Raynox lenses are clip on magnifiers that attach to the front of your camera and these are popular as a relatively inexpensive way of adding a much closer focussing ability to your camera.
A hand lens is essential for plant identification, and can be a major asset for invertebrates too. Being light and small you can carry it with you at all times. They aren't expensive but ensure you get a glass (not plastic) lens. x10 is a good starting point. Some have multiples lenses that can be used separately or rotated together to give various magnifications.
For most invertebrate identification, a stereo (or binocular) microscope is necessary. Stereo microscopes have two eyepieces so you can view your specimen in 3 dimensions. If you haven't used one before then prepare to be amazed! A good basic model starts at around £130 so they are not too expensive. See the microscopy page for me details.
A pond net is essential for finding aquatic life. A white plastic tray is usually used with the net so you can empty and examine your catch in this.
Sweep nets are useful for catching small invertebrates hiding in vegetation.
Pots and tubes
Most serious recorders will need to bring home specimens to examine (and identify) at home, usually with access to books and keys as well as a microscope. These are sold in every size and shape but keen recyclers can often find their own from small food containers, etc.
Where to buy?
The following are just a few suggestions:
Natural History Book Store - sells just about everything mentioned on this page!
Field Studies Council - excellent range of ID books and leaflets.
Watkins and Doncaster - lepidopterist supplier, plus general entomology equipment.