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Thank you all for your replies.
She's adamant that they did not ask for the purpose of the loan during the online application. They asked only during the follow-up phone call. Curious, but there you go.
Having only achieved a good credit rating in recent months due to her job, she doesn't have a sufficiently high credit limit to buy a bike on the credit card she has currently.
Davebro, I'm of the same opinion. It doesn't make sense and was speculation on my part. I'm clutching at straws here but the loan company are adamant that they won't explain why the loan was refused.