"A couple of Sundays ago at just past 11am my mobile rang. An automated message purported to be from Barclays Bank, querying a payment to Argos for more than £1,000. Not only had I not made a payment to Argos recently, nor do I bank with Barclays.

I am plagued with these kinds of calls. Usually, when possible, I make it clear to the scammers that I know their game. Usually, that call ends there and then.

But this time I realised there was a chance to string them along. It was just a question of how soon they realised I was bluffing. I assumed it would be a couple of minutes. In fact it was three hours.

I called the number shown on my phone and, pretending to be a confused, doddery old man – not that difficult for me – I expressed the expected alarm at the bogus payment.

The man who answered, who had more or less a received pronunciation accent, went through what I understand is the usual story: my credit card had been compromised, bankruptcy was on the horizon, remedial action essential. Someone from the investigations team would call me back, he said. Thirty minutes later someone calling himself "Adam" rang. From here on in the number always came up as "No caller ID".

Several times Adam ended the call, presumably to consult his fellow crooks, and rang back later.

First, Adam went through several security-like questions. When did I last use my credit card? "Can't remember," I replied. What was the last transaction I made? "Dunno." Did I use internet banking? "No". Then came the big one: how much is in your current account? "Around £80,000," I said. (If only.)

There wasn't a sharp intake of breath. I couldn't hear a licking of lips. But I could sense that Adam's vocal cords had tightened, and he was from now on more intense.

He explained it was a matter of the utmost urgency my credit card should be cancelled and a new one issued. Would I like to keep the same pin, he asked? I said "yes" and he asked for it. I'd already written down a made-up pin on a bit of paper, and gave it to him. I thought I could sense him trying hard to remain matter of fact.

He asked if I had my debit card and credit card with me. I said I couldn't find my credit card. Adam was stern, insisting I look for it. I couldn't be bothered to fabricate two false 16-digit numbers, and so I told him my wife must have it and she was out. He let this go.

I had already taken out one of my debit cards from my wallet, one issued by HSBC, jotted down the first eight digits and made up eight more. To my surprise, and some alarm, Adam read out the first six digits, correctly, saying the card was issued by HSBC. (How did he know I had an HSBC account?)

He didn't bother to explain why he needed the debit card, too – or why he needed the numbers – and, being in character I didn't ask, just went meekly along. I guess the implication was that both cards were compromised and so the investigations team needed to cancel that one as well.

I gave him the made-up number, thinking this would be the end of it. But within a minute he came back and said the number I'd given didn't seem to be a genuine one.

I assumed concerned bafflement and told him that all I could say was that I was reading out the number on the card in front of me. There was another pause, presumably while he consulted one of his scammer colleagues. To my surprise they decided to keep going.

As this was Sunday, as Adam pointed out, the banks were closed. So the only safe procedure was to send round a courier to pick up my debit card – right now. It couldn't wait until tomorrow. Was that OK with me? I told him it was fine.

He said I should put the card in an envelope and address it: HSBC Investigations Team, what he thought was my name, Ref HS844677.

He was most insistent on two things: he repeated several times that the courier must, on no account whatsoever, be able to see that a bank card was in the envelope, and that I must seal it extremely carefully.

He insisted three times that I read the address back to him. I pretended to be getting a bit fed up with all this but he explained, quite firmly, that banking security was at stake here and there was no room for error.

A new thought then occurred to him. Did I have a current bank statement, and could I find the most recent one? I noisily opened and shut a drawer. He asked for the balance. I had already written down a precise made-up amount. I told him £81,224.93.

Adam told me he'd ring back when he had booked the courier and got an ETA. He'd already asked me for my postcode and I'd given him one where I lived several years ago. Now he asked for my exact address and I gave him a house number that I knew was too high to exist in that street.

Fifteen minutes later he rang back, sounding a little flustered. A blue Prius was outside the address I'd given but it seemed to be a block of flats. "That's not right," I said, "I live in a house." Another hiatus, as he communicated with the courier. Could I see a blue Prius? he asked. I paused long enough to have looked out of an imaginary window and said "No, I can't see a blue car".

What can you see outside your house? he asked. "Nothing," I said. He rang off again.

Five minutes later he called back. Would I mind going out and trying to find the blue Prius? I explained that I had a bad leg and couldn't leave my house at all. But I would gladly open the front door and have a look. Then another call. The driver was absolutely adamant that the address was in a block of flats.

I'd kept this charade up for a lot longer than I'd expected and I was about to go out. "Oh dear," I said in my best whispery voice, "it looks like I've been wasting your time."

What? I switched into my own voice to deliver the – unprintable – coup de grace, and hang up.

Adam even had the cheek to ring back later. I didn't answer. I wish I had. I could have thanked him for the afternoon's entertainment.