‘I was on a camp bed,’ I tell her, a lie so instantaneous that I have no sense of its origin. ‘Kept waking up every two hours, couldn’t get back to sleep.’

‘Then you should have stayed in a hotel,’ she says, as if I have been both stupid and unreasonable, and not for the first time it occurs to me that we are entering into a discussion entirely without basis in fact.

‘Well, I thought about it,’ I tell her, ‘but my friend would have been offended. I hadn’t seen her in years.’

‘You were staying with a girl?’

Now why did I say that?

‘Sure. Not a girlfriend. An old flatmate from university. She’s engaged. She has a boyfriend.’

‘I’m married,’ Sofía replies curtly, and it will now be at least ten minutes before the clouds of her jealousy subside.

We begin on the ground floor, ostensibly shopping for handbags and make-up. There are a few small reflective surfaces in the department but nothing to compare with the full-length mirrors upstairs in men’s and women’s fashions. I keep a constant look-out for faces and try to recall as many of them as I can before suggesting to Sofía that we take the switch-back escalators up to Level One. These are perhaps the best surveillance traps in the entire barrio. For a start, they are mirrored all the way up, allowing any number of opportunities to observe customers moving up or down on parallel stairs. Better still, they are situated in the centre of the building. It is therefore possible between floors to make an apparently wrong turn into a department, to spin around, briefly check the escalator for a tail, and then continue in the opposite direction. That’s exactly what happens on Level One, where Sofía even adds a note of unwitting authenticity by grabbing my arm and saying, ‘No, not that way,’ as I turn left, rather than right, into women’s fashions. She picks out several dresses and I buy two for her with the cash left over from Alfonso. At this point her mood visibly improves. Then we go up to Level Two where Sofía insists that I try on an array of Eurotrash jackets, most of which, she agrees, make me look like an Albanian pimp. Still, she’s determined to buy me something and it is with a sense of foreboding that we head towards Ralph Lauren. In Spain, the pijo look – Polo shirts, pressed chinos, tank tops – is considered the height of fashion among the more conservative classes, and Sofía finds no irony in recommending outfits that would have me beaten up in Notting Hill.

‘What are you trying to do, turn me into your husband?’ I ask as she passes yet another striped shirt through the changing-room curtains.

‘Just try it on,’ she says. ‘Don’t be so trendy, Alec.’

Eventually I settle for a jumper, endlessly checked in a full-length mirror providing almost total coverage of the men’s department. There’s no sign of the girl in pigtails, nor of the man with the carrier bags. Laden with shopping, we then leave via the exit on Alberto Aguilera, looping back towards the main entrance at Argüelles metro before proceeding east down Princesa. The walk offers conclusive proof that I don’t have a surveillance problem; in almost an hour of dry cleaning I haven’t noticed anything to arouse my suspicion.

Back at the apartment, Sofía makes lunch but shows no interest in going to bed. I am secretly glad of this, but irritated none the less by the sock to my vanity. Although she has never mentioned it directly, her sex life with Julian is clearly abysmal and I relish my role as the handsome young buck, Pyle to his Thomas Fowler. Instead we take a cab to the Prado, Sofía bombarding me with a series of uncharacteristically aggressive questions en route.

‘How come you didn’t answer your phone when you were away? For ten days you haven’t talked to me. Is it because you were sleeping with this girl?’

I respond as calmly as possible, sensing that she is picking a fight for the sake of it, yet the presence of the taxi driver is unnerving. I am naturally reticent and closed and loathe holding potentially embarrassing conversations in the presence of strangers. Perhaps on this occasion, however, it is a blessing in disguise; were we back at the flat I would certainly accuse Sofía of hypocrisy and encourage the conversation to escalate into a full-scale row. Who is she, after all, to accuse me of infidelity when she shares Julian’s bed, night after night?

‘Can we talk about this later?’

‘No. I would like to talk about it now.’

‘You’re worried about me going to bed with another woman? You think I’m seeing somebody else?’

‘I don’t care who you see,’ she says, unconvincingly. The cab slides across two empty lanes in bright sunshine. ‘I just care that you don’t lie to me.’

‘Well, that’s reassuring. Thank you. This is turning out to be a terrific afternoon, just what I had in mind.’

Perhaps we have arrived at adultery’s inevitable final reel: it can go no further than mild escapism. Sofía cannot respect me for what I have done to Julian, and I cannot respect her for betraying her husband. She wants nothing more from the relationship, and I have nothing left to give. It has all gone on for far too long. We have absorbed one another’s lies.

‘What is this about, Sofía? What is it that you want?’

A withering look. ‘Qué?’

‘If it’s not worth it, if you’re not having a good time, then why did you agree to meet me today? Just to have an argument?’

Silence. The driver swings the taxi around the fountain at Cibeles and it’s obvious he has one ear on our conversation. I switch to English.

‘If you want to end it, then end it. Don’t make me do it, don’t make me into the scapegoat.’

‘The what?’

‘The fall guy. El cabeza de turco. It’s an expression.’

‘I do not want this to end. Who said that it was ending?’

‘Then let’s not fight. Let’s go to Vermeer. Let’s enjoy the afternoon together.’

‘I’m just tired of all your stories, Alec,’ she says. ‘I don’t believe them. I don’t believe you went to England. I don’t know who you are.’

It is like being with Kate again, a hideous recollection of the last time we saw one another at her house. Stupidly I say, ‘I can be whatever you want me to be,’ and Sofía looks at me with utter contempt. ‘I don’t mean it like that. I mean this is supposed to be fun, otherwise why are we doing it?’

‘Fun?’ she says, and it appears as though she might laugh. ‘You think that’s all this is for me? Fun?’

‘Well, what more can I ask for? I am faithful to you. I went to London for a wedding. I didn’t sleep with Anne. You’re married. I don’t know what else to say.’

The cab stops at a set of traffic lights beside the Museo Thyssen, about 500 metres short of the Prado. We’ll be there in under a minute, but time might as well have stood still. Very quietly, in English, Sofía says, ‘I love you, Alec,’ the first time she has spoken these words. The mixture of dread and exhilaration they engender, the flattery and the panic, leaves me speechless. I take her hand gently in mine as she turns away and looks out of the window. I touch her neck, her hair, and wonder what to say.

‘How much is it?’ The driver pulls over to the side of the road. We’ll get out here.’

I hand him a fistful of change and we emerge in silence. Gallery tourists are taking up most of the pavement, with their money belts and their litre bottles of water. Sofía follows me, her face flushed red, eyes brimming with sadness. I want to hug her but cannot do so for fear of being seen.

‘Just forget it,’ she says. ‘Forget what I have said.’

‘How can I forget it? I don’t want to. You just surprised me, that’s all.’

‘I surprise myself.’

To reach the Prado we have to cross the road at a zebra crossing. Years and years ago, Kate and I took this exact route on a long romantic weekend in Madrid, holding hands and laughing. I spent an hour inside looking at exquisite portraits by Titian and Coello; she went for late Goya and Hieronymous Bosch and I thought at the time that this said something worrying about our relationship. Sofía walks about five feet ahead of me, passing a line of stalls selling trinkets and bullfight posters, and folds her arms across her body.