I tried getting both the chat support and the UK applecare rep (was careful not to give my full name and requested the query not be connected to my account) on the phone to unpack the following sentence:
A consumer is also entitled to withdraw from the contract by returning the product in exchange for a full refund if the consumer rejects the goods within 30 days or if the product does not conform with the contract after one repair or replacement.
They were very careful about committing to anything and didn't offer an explanation for what happens if there have been multiple repairs done already.
I was able to learn that I need to contact the place of sale to make a claim under consumer law. This would be the applecare phone support for me since I purchased my laptop online.
I was hoping they'd say, "well if a product as been repaired 4 times then you'd qualify for a replacement" but they seemed careful to avoid that.
After this I went on to call another Apple Store. The employee asked me right away if "I'd lost confidence in the machine", to which I replied yes. After learning about the number of repairs he went on to recommend calling applecare support. He gave the reason that they have 'more options' than those in store.
I think I've got to the limit of what I can do anonymously - either going into the store or calling applecare and giving my details opens me up to getting notes on my account. I can't see any other options so will try that tomorrow sometime.