Here's an update on how it all went! (next time I'll try to use the diary)
CABLE
I was originally hoping to use 2.5mm cable over a distance of 120m but ended up buying some 4 core 10mm armoured cable costing £130 OUCH off ebay -as its 4 core, I assume it means its the equivalent of 2 core 20mm?. But I took the advice to think of it as an investment. This came in a large drum of 150m. And being 4 core means I'm now well inside the voltage drop limit. I decided not to cut the cable, so I can maybe use it again in another project later. I then went around the garden rather than under it. I think I'm glad I did it this way.
BATTERIES
I was originally planning on using one 17ah battery that I had as part of 'Jump Start' and just use it as a voltage regulator and not worry that it couldn't really store the energy, having the laptop do the storing. In the end I bought 4 27ah 'New' AGM batteries off ebay with the expectation that these would store much more. These should have a 10 year life according to the spec, but when they arrived they were not new :-( but 7 years old and just never used. Consequently they all read 6v or theabouts. After contacting the seller he refunded my money which was nice, and I spent 2 weeks trying to coax them back to life. They now work, but I'm really dubious that they hold 100ah between them. More like about 20 I should think. My learning is that I'll ask more questions next time! Anyway, I guess it worked out for my learning phase.
PANEL
I was going to go with a 20w panel, but this really failed to charge the batteries enough each day, so I was seeing them drop to 40% too quickly. I used the laptop a lot less to compensate, but in the end that was too much hassle, so I upgraded to a 60watt panel. This works much better
CHARGE CONTROLLER
Always planned to have one :-) but my 5amp cheap Maplin one broke after 2 weeks. I upgraded to another cheap one, but 10amp. It has some nice features though for the £20 I spent on it, so I'm happy here.
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NEXT STEPS:
I think I need more battery or more panel for winter (or both) I have some panels I can use, but would need to buy batteries, so I plan to plug in my other 55w panel in winter, or the additional 20w panel. I'm also upgrading the socket in the kitchen from a standard 12v car socket to one with a USB port as well to charge up the mobile phones from.
Thanks for the advice so far. More pics and a bit more information is on my website if you're interested: www.suburbangoodlife.com/energy