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Our camera has a lens about 2 inches long when it pops out and magnifies far better than my 4" binoculars.
So technology must have marched on.
Can I get anything for £100?
I have a pair of Nikon 10X25 Travelite Ex Binoculars
http://www.amazon.co.uk/Nikon-10X25-Travelite-Ex-Binoculars/dp/B000FFP154
The are plenty of sellers and they are around your price point. I got these to replace a pair of early 1990s Nikon Travelites because I'd droped them and they got a bit out of whack.
Pushing your budget a bit and not really small but the RSPB Avocet bins are excellent
I have a pair of these:
Superb they are and very small.
Want something a bit bigger - I have a pair of these also:
http://clearviewbinoculars.co.uk/acatalog/Visionary_Freebird_8x42.html
and they are astonishing for the money. I have put them up against some seriously expensive bins (think £800+) and yes there is a difference but its marginal.
Note I am a keen astronomer, bird watcher and photographer and can judge a good optic...
What magnification do you need and are binos actually required? I had a similar requirement and went for a Vortex monocular in the end: [url= http://www.vortexoptics.com/product/vortex-solo-rt-8x36-tactical-with-reticle-focus-monocular ]One of these[/url]