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Eventually, they followed a staff sergeant into a room dominated by a dark oak table. They were requested to sit down, one at each end and one in the middle. A pencil, a sharpener, a ruler and a rubber were visible at each position, together with the examination papers.

‘Ladies, you have an hour and a half to complete as many of the questions as you can. There will be no conferring or talking. Do I make myself clear?’ asked the duty staff sergeant.

They glanced at each other.

‘Yes, quite clear,’ they replied, one after the other.

He raised his arm and stared ostentatiously at his watch, then smartly lowered it and gave the instruction: ‘Up pens, begin.’

Hilda turned the paper over to read the questions before starting to work on them. Part 1 consisted of fractions, divisions, multiplications and subtractions, an easy starter. Part 2 was geometry, part 3 trigonometry. Part 4 was a series of algebraic equations. Long ago in school, similar problems had been dubbed bread and butter sums, and more recently, she had supervised Otto’s mathematics homework. She lifted her pencil and began the calculations with confidence.

She decided to start with the more advanced questions. If she ran out of time, it would be better to have omitted the simpler ones. She sharpened her pencil without checking whether it needed to be. One trigonometry question sent her mind off at a tangent; she was required to calculate the time it would take a cruiser sailing at thirty-five nautical miles per hour to come to the aid of a sinking ship at point B, while evading U-boats at positions C and D. The radio messages giving coordinates of the convoys came rushing back to her.

She shook off the unwelcome memory and began to enjoy this new challenge. Once more, she recalled sitting with Otto, guiding him through mathematical hoops. When she looked up at the wall clock, she saw she had almost an hour left. She turned to the geometry paper. This was something she relished; she tackled the questions with ease.

Next up was the algebra. The equations and formulae came back to her like a mantra, and when that page was complete, she had a little more than twenty minutes to finish part one of the papers. She took great care over this part; a slip here might persuade an examiner not to pursue her efforts any further. Yet the questions were embarrassingly easy. Hilda supposed the entire exercise was designed to rate the three of them, but there was still no indication of what came next.

Hilda read her answers to herself, checking the logic she had applied to each question. She was satisfied that her efforts had been diligent and her answers were correct; at least she had done her very best. She put her pencil and ruler down and gazed at the second hand of the large clock at the end of the room as it counted down the last couple of minutes.

‘Time, ladies, pencils down,’ the staff sergeant said, approaching to gather up the papers and make sure their names were on the top of the front pages.

‘Please take a seat outside. You will each be called to interview with Sir William Raeburn in alphabetical order: Baker, Campbell, and then Wheeler.’

‘Always last, the problem with being a Wheeler,’ one of the Wrens said.

‘Madam, if the first may be last then surely the last may be first? I shall reverse the order. Miss Wheeler, you will be first,’ said the staff sergeant with an air of superiority. Miss Baker, this time you will be last.’

It made no difference to Hilda. She would still be in the middle. She would have preferred the interview first, thereby freeing her up her afternoon but that was never going to be an option for her.

Miss Wheeler’s interview lasted almost twenty minutes. Now it was Hilda’s turn to face this man with a distinctively Scottish surname. Perhaps that was a lucky omen.

Sir William sat at the end of the room. His head bowed over his hand, while he scribbled on a sheet of paper in front of him. He had white hair, a neatly trimmed coiffure. He wore a dark suit, a gold waistcoat spattered with black spots, a white shirt and a dark blue tie. The pen was in his left hand; his spectacles dangled from a cord on his chest. He ignored her for a few moments, allowing her to appraise him and to ponder on what this interview intended to achieve. He put down his pen, and without raising his head, he barked.

‘Frau Richter, sit down.’

She was taken aback by his words. She sat down as she was bidden on the hard-backed chair opposite him. This man clearly knew her background. Was he merely showing her he did, or were his intentions more sinister?

‘You are German. We are at war with your country. Why should I not lock you up for the duration of the war?’

Her knees tensed, her pulse rate rose and she felt blood rushing from her face. ‘My country is Scotland, my loyalty is to the king,’ she said firmly. ‘My preferred name is Hilda Campbell. I have specific qualities which this country needs.’

He grunted. ‘Your son is in the German army and you have a home in Hamburg. Or is that a fabrication, a lie?’

She swallowed hard. It appeared he knew much about her past but very little of her recent activities.

‘Yes, I have a son in the German army and he has access to our old home. I am a widow. I do not deny any of this. I have lived under the appalling regime which the Third Reich has become. I was housebound in the First World War, but I would not be treated so gently in the present climate in Germany. Hitler will stop at nothing. He is not just a menace to Great Britain; he is a menace to the world. I will play my part in defeating this terror, even, if you insist, from a British prison. Sir, your assessment of me is misplaced.’

It was a struggle to control herself, but she managed to keep her voice steady and unemotional. The interview had hardly begun, but she was now prepared to give as good as she was getting.

Sir William Raeburn homed in on her Achilles heel. ‘You were sent to Portugal by Herr Eicke of the Gestapo. You provided intelligence to the enemy. This is a treasonable offence.’

She did her best to stay calm but her legs were shaking. ‘I do not deny being a double agent. I had to carry out Eicke’s instructions to avoid becoming a suspected thorn in their side. If I had not, I am confident that I would not have survived. I did send one message to Berlin, to earn credibility with them, but I was also instrumental in identifying a German spy ring based in America. Why would I have done that if I was a German spy?’

It was growing harder and harder to remain calm, especially when he launched his next sally.

‘Why were you awarded an Eagle Civilian Cross with two crossed swords?’

God, she felt she was being turned over like a pig on a spit. She was appalled to find he knew that, but she refused to flinch or show any weakness. She lifted her chin and struck back.

‘It was given, not awarded, to retain my loyalty to the Reich and for the information I provided to them, the false information MI6 prepared for me. It was not for anything I had done for the glorification of the Reich. I have been open with MI6 about that, as well as everything else I have told them.’

Her eyes welled up and she groped for a handkerchief, hoping against hope that he would not see it as a sign of weakness. But he did.

‘Crocodile tears?’ he jeered.

His rudeness was cutting and heartless, and she offered no riposte. She hated this man. This was not an interview; it was a nasty interrogation, on a par with Gestapo questioning.

‘How else can I convince you of my loyalty to this country?’ she demanded.