YBR125 electrics fail to start

[nickchips]

First just thought I'd say hi since this is my first post. Have been lurking around reading for a while but haven't posted yet, so hi everyone!

27yr old first time biker as of three or four months ago.

I've got a YBR 125 custom 2009. Bought it second hand and luckily it did actually run . Everything seemed fine for the first few months. I then had a minor fall in some torrential rain which resulted in some expensive repairs (and lessons very much learnt!) but it's been running fine since. Then last week, it just failed to start...

Turning the ignition would give anything between no power at all, to everything coming on (lights, dash, engine warning light turns on then off). But, on occasions where it appears to start, starting the engine with the electric start kills all power instantly. The starter appears to 'click' but power goes dead straight after. Interestingly, pulling the front brake has the same effect, so I imagine its that any drain on the battery (starting engine or turning on brake light) kills it. The dash lights would actually fade on/off sometimes when trying to start or wiggling the steering which makes me suspicious its a dodgy wore somewhere.

If the neutral light does come on, it will start fine with the kickstart (luckily, since I had to drive it 4 miles home after the first time it stopped).

The battery is theoretically 2 years old, though who knows in reality. I've got a haynes manual so have done a bit of testing following that:

• voltage across the battery seems fine (a little over 13v).
  
• battery doesn't look damaged. cleaned of a little bit of corrosion on the positive terminal.
  
• took the front light off and tested voltage to the ignition via starter motor which seems fine.
  
• tested continuity through ignition switch, no resistance.
  
• checked continuity in battery neg to earth/frame wire and that seems good.
  

Any tips on what to do/check next greatly appreciated! I can't find any info on actually checking current from the battery. Im no mechanic or electrician, but I imagine it can hold charge and still not be supplying sufficient current...

I think I ought to just get the battery properly tested (and maybe replaced)... any recommendations where to do this (cheaply!) in London, UK?

Cheers in advance, I'm itching to get back on the road!