Just an observation -
the transformer appears to be labelled as a 220V AC input, 12V AC output.
If built/used in the UK it (the transformer/rectifier part) will have around a 15V DC output feeding the LM317 and, with the internal volt-drop requirement of the LM317, would give an (approximate) maximum 12V DC output (variable from around 1.2V as a minimum).
The 220V AC transformer can be safely used on a 110V AC supply but the output will be HALF thereby the DC output after the LM317 will only vary between around 1.2V and 6V DC.
Junk the transformer. Fit a socket that accepts the DC supply from an old laptop power pack (commonly 19V DC output) and you'll end up with a power supply that varies from 1.2V to around 16V SAFELY.
Note - the DC output from the laptop PSU can feed directly into the power supply board where the AC (from the transformer) used to go (in which case polarity isn't an issue) OR you can remove the rectifiers (four diodes) and apply it straight to the smoothing capacitor but you MUST get the polarity right!
In my experience I wouldn't trust the spec or quality of the transformer in such kits - the rest of it is par-for-the-course but using a laptop PSU is far, far safer and gives you a much more reliable and wide ranging output.