Miss Reece was a knighthood vetting official who worked for the Cabinet Office.
She was tasked with vetting Philip Burton for a knighthood but was not told about the line of work at the Anomaly Research Centre due to the Official Secrets Act. At some point she contacted Jess Parker to arrange a interview with James Lester to discuss Philip's background before he could be knighted. However, Lester was under the impression that the knighthood was for himself so he talked his and Philip's friendship up, unintentionally dismissing any doubt Reece had about Philip's background. As Reece was leaving the ARC and thanking Lester, he relised she had been vetting Philip and not himself. (Episode 5.1)
Either Miss Reece change her mind about knighting Philip or he died first as he was never knighted before his demise. (Episode 5.6)