I had fixed to meet Alexandra Richards on the beach at Littlehampton. Just by the East Beach Café. That’s a multi-award-winning building designed by Thomas Heatherwick, which looks like the rusty shell of some primeval mollusc. It’s one of the town’s proudest boasts, another attempt to smarten Littlehampton up. But the resort’s ingrained tackiness has always resisted the march of gentrification. The Waitrose that opened there didn’t last long.

There’s a car park next to the café. Alexandra and I agreed that we’d discuss her problem as we walked along the front, then maybe have a coffee on our way back to the cars.

She looked somehow faded. I would have put her in her forties, maybe early fifties, getting on for my age. No wedding ring, and she made a point of telling me, almost as soon as we’d said hello, that she lived alone, she’d never been married and didn’t have any children. She needed to get that one out of the way quickly.

The she gave me a short résumé of her life. She’d been a teacher, an experience which she gave the impression she hadn’t enjoyed much. A legacy from her grandmother had enabled her to give that up and now she did some charity work. Unspecified charity work.

Tall, slightly lumpy, with a pale freckled face and biscuit-coloured hair that didn’t quite qualify as auburn, Alexandra Richards wore the kind of clothes that had been chosen not to draw attention to herself which, perversely, made her look slightly eccentric. And drew attention to her. A beige raincoat, though it was a warm May day, and almost-masculine brogues.

The tide was low. The beach at Littlehampton slopes very gradually. High water reduces it to hillocks of uneven shingle, while low tide exposes acres of cement-coloured sand. Swimmers have to walk out a long way before the water reaches even their waists.

Had it been high tide we’d have walked along the promenade, bordered by a strange piece of artwork made up of wooden slats, some painted in bright colours and claimed to be the ‘longest bench in the world’. But that time of day we could go on to the sand. I suggested to Alexandra that we walked to the right, towards the mouth of the River Arun.

Her appearance had made me suspect she might be shy, but she turned out to be very forthright. Almost dogmatic.

‘It’s got to a point,’ she said, ‘where I realize I have to do something about my mother.’

‘How old is she?’

‘About to be seventy-five.’

‘Does she live with you?’

‘God, no.’ The thought actually made her shudder. ‘She lives on her own.’

‘How is she mentally?’

‘All marbles in place. Or perhaps I should say that she’s as sane as she’s ever been.’ The line was deliberately ambiguous.

‘And your father?’

‘I’ve never seen much of my father.’

‘Ah.’ There was a whole history there, but it wasn’t the moment to investigate it. ‘Where does your mother live?’ I asked.