First of all the wiring should be the first thing to rectify. There should not be any of the conductor visible.
Your installation is slightly unusual to us here in the UK as you are using both sides of the changeover contact (NO, Normally Open and also NC, Normally Closed) However, the Single Channel version of the Hive provides exactly the same switching functionality as you have now, so it shouldn't present a problem.
The first part is fairly easy.
The photo inside the lid tells you what the present terminals are, but first check that the terminal marked L is a permanent live at mains voltage, just in case your system uses a voltage other than 230v. If it is 230v, then the below applies if it is something else eg 24v post back for further advice.
A = Permanent Live
B = Heating on (Normally Open)
C = Heating off (Normally Closed)
If you look at the Hive, you can find corresponding terminals.
L = Permanent Live
3 = Heating on (Normally Open)
2 = Heating off (Normally Closed)
You will then need to add a link wire between the Hive L and terminal 1 (Common)
The next part could be more difficult though.
Because your existing programmable thermostat is battery operated, it doesn't need a Neutral so there may not be one there for you to use. However, the Hive being mains powered does need a neutral. The cut off blue wire may be a neutral but you will need to trace it back to see where it goes, and if you can connect it to a neutral.
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Further Answers please in UK section - there are more there so far.
http://www.diynot.com/diy/threads/hive-installation.474634/#post-3811076
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