I'm hoping someone can point me in the right direction here, especially anyone who works in the banking industry. I'll try to cut a long story short :-

Back in September my son booked a flight from South Korea to UK scheduled to arrive on 19th Dec.
He booked online through a company called BudgetAir, and used his Visa debit card.
In early October, he rang BudgetAir to cancel the flight and rec'd an email from them explaining that he must tell them his name, flight confirmation number and dates of travel.
They told him he would have to pay a cancellation fee of about £100 which he agreed.
Their email stated it could be 8-10 weeks before it would appear credited back to his card.
He sent the req info and waited.
On 28th December he rang them to ask about the refund and was told that his emailed response had not been received and therefore his ticket was treated as a 'no-show' and no refund will be given (he has the letter emailed to them in his sent items dated 7th Oct)

Now, they have said they will only give him a £95 refund and they are still saying he was a 'no show'.

I told him to do a dispute through Visa, however Barclays tried to say that he has gone past the acceptable 8 week time frame in which someone must file a dispute. I don't believe that the dispute started 8-10 weeks ago, in my mind it began on 28th December. There was no dispute until after 10 weeks or more had elapsed with no sign of refund.

Does anyone here have any idea how my son can start to recoup the £650 that he's legitimately owed?

I might have got some of this wrong (unlikely, but it has been known to happen )

Now this is UK law, so might be different if he's claiming under USA rules.

The time limit for disputes is usually 60 days (the eight weeks they talk about), however this is from the date the transaction appeared on his statement, so the booking in September might not have been on until Oct meaning that his time didn't run out until Dec (which I'm guessing is what the airline were counting on), he might however have dropped lucky and it not be on that month but the November one, in which case he's well inside, however this isn't all he is covered by.

Chargebacks are valid for 120 days, and furthermore (as certain items such as holidays are booked well in advance) it starts on the date of the expected service (in his case the flight in December), so he can try that.

Lastly he has Section 75, which makes Visa jointly liable for the debt, by them refusing to get involved and passing on the complete liability to your son they would be in breach and usually give you the money back fairly quickly when you ask them for the complete financial details of the transaction (which you are entitled to) as you want to refer it to the FSO (tend to have your money back by the end of the day).

If he gets stuck give me a shout and I'll dust off the old law books.

Are Visa still jointly responsible with it being a debit rather than credit card.

Easy to say now but I'd always send things like this via recorded delivery.

And that will teach me to answer late at night.

As it's a debit card section 75 doesn't count, you should still be able to get it as a chargeback though.

Did he get any sort of confirmation email or letter of his request to cancel, other than a reply to his initial inquiry?

The only email he got (and sorry I don't have a copy to quote exactly) was BudgetAir saying how sorry they were that he was cancelling his flight and would he please give them the flight confirmation number etc etc. He had spoken with someone on the phone to initially cancel, they then explained the penalty for cancellation and subsequently sent the email.
Unfortunately once he'd sent the response with all they'd asked for, he didn't contact BudgetAir again as they had explained it would take 8-10 weeks for the refund to appear. He assumed they had received the email as they had done with all others he'd sent, and no reason to think otherwise.
I suppose you could say that he should have confirmed via phone that they did get it

I fully understand the 60 day time limit rule and as I'd said, in my mind there was no dispute until end of December because up until that time, technically there was no question of him not getting a refund. It only came about when he rang them and they began the whole "we didn't get your email with all the original flight details".
Up until that time, he was abiding by the BudgetAir guidelines of having to wait up to 10 weeks for the refund.

I'll keep you posted as to how he gets on with it all, and thanks for your expertise

One more thing to add to this is, they offered him £95 refund.

IF, as they are claiming they had no knowledge of the cancellation, and treated the ticket as a "no show" why would they offer any refund at all?

Gesture of goodwill?

If you cannot prove you sent a cancellation then they can easily claim or honestly say they never received it and may have just assumed that the cancellation fee of £100 was too high to pay and you'd go ahead with the flight.