which telephoto lens should I buy?

Assuming you're happy to spend the £1.5k some of these options cost, it sounds like it's all down to lens performance.  That's not just about sharpness, also consider AF speed and minimum focus.  The fastest two on your list would be the 100-400 Mk2 and the 400mm non-IS prime, so if you plan to do a lot of in-flight shots, go with one of those.  They're also light enough to easily wave round in the air tracking birds.  In addition to that, they're light enough to carry long distances should that be the way you tend to go birding (ie if you're sat in a hide, the weight isn't so important as it is when you're hiking in the mountains).  The 500mm f/4.5 has one big drawback - it isn't an f/4.  If it was an f/4, you could add the 1.4x converter and get a 700mm f/5.6 lens, giving you valuable extra reach with AF.  The Sigma will break the f/5.6 barrier and therefore be MF only.

Have you tried using the 300mm f/4 you have with the 1.4x to see if 400mm is adequate?

I can only comment on the Canon 400mm f/5.6 prime which I use and find it to be a fantastic lens. When you get it right the images are very sharp indeed and the autofocus is super fast. As WJ has already said, it’s a fantastic ‘bird in flight’ lens and as I don’t mind taking a tripod or monopod with me it also produces great images at lower shutter speeds when mounted. In terms of negative sides to the lens its close focus distance is around twelve feet and it doesn’t have IS. I had taken these negatives into consideration and have never regretted buying the lens. My Flickr link is below if you perhaps would like to see the results I’ve been getting with it.

Another one of our members (Hazy) has recently bought the 100-400 mkII and has been getting some fantastic images with it, I’m sure if she sees your post she’ll tell you a bit more about it.

Hello Paul. My OH has the canon 400mm f/5.6 prime and I have the canon 300 f/4 prime which i sometimes use with a 1x4 converter, both in my opinion are excellent lenses. I am definitely no expert though :(. I cannot see the difference between the 300 and the 400 even when the 300 is used with a converter, but the 300 close focuses and can sort of double as a macro :) Cannot comment on the sigma as not seen it sounds great though but very heavy

Hello Paul b,    I recently purchased the Canon EF 100-400mm f4.5-5.6 L IS II USM Lens  upgrading from my previous Canon EF 70-300mm f/4-5.6L IS USM  and all I can tell you is that I noticed a significant difference in sharpness, showing excellent feather detail on the 100-400mm mkII    and have been very happy with it.   In addition to this lens I have the 1.4 x converter which will still auto focus using the centre point which is a big bonus and of course, having Image Stabiliser helps give a steady crisp shot.      I'm not an expert at all on camera gear but can recommend the Canon EF 100-400mm f4.5-5.6 L IS II USM Lens  as an outstanding quality lens without going over the £ 2 k  mark.     If you asked me what lens I would really like  ( lol  !!  )   then it would be the Canon EF 300mm f2.8 L IS II USM Lens but being £4799.00  I will have to dream on  !!!      Good luck with whatever lens you opt for.    

post edit:   Paul, you may want to take a look at different photos taken with the 100-400m  mkII     HERE

As others have mentioned, the minimum focus on the 300 f/4 makes it handy for close up stuff - and the new Mk2 100-400 gets closer still.  The new lens is so good (despite being a zoom), I'd definitely recommend it over the 300mm now (unless, like Hazy, you hanker for the f/2.8 version!).  Between the 100-400 Mk2 zoom and the 400mm prime?  Difficult - the prime's cheaper and lighter, the zoom's got an excellent IS and close focussing.  If you're buying one lens and can afford it, the zoom's the better bet in my opinion, but either will give you superb results.

Of the Tamron & Sigma 150-600mm I'm not so knowledgeable.  You get more length, but at a price.  The f/6.3 aperture at long lengths can slow down AF a bit in poor light and the minimum focus doesn't lend it to the sort of close ups you'll get with the 100-400.  They're heavy too, which can be bothersome.  But all three of the 150-600mm lenses are an excellent choice and are capable of great results, it all depends what's most important to you.

A note on Hazy's comment re AF with the 1.4x attached.  The 100-400 (or 400mm prime) with a 1.4x attached becomes an f/8 lens.  It will AF (centre points) on a 5D3 or a 7D2, but not on your 7D or 600D

One further thing on the 500mm f/4.5 prime - you'll need a decent tripod to use that.  It's not really a handheld lens!

It doesn't always help seeing images from different lenses as too much depends on the camera, photographer etc, but a selection...

100-400 Mk2 + 1.4x on a 7D2

100-400 Mk2 on a 7D2

300mm f/4 on a 40D

400mm f/5.6 on a 5D3

I'm feeling rather drawn to the Sigma 150-600mm, the contemporary rather than the sport (for weight reasons). Been very happily using my 300mm f4 with 1.4x converter for five years but you know how it is, a little more reach would always be nice...