If she's allowed to make an appointment at any PEO not just Croyden, might be worthwhile to find out if any others have appointments available. It's probably worth an overnight trip somewhere to get this sorted.
Good point, make sure you check the rest of them:
Public Enquiry Office - Birmingham
0870 606 7766
Dominion Court, 41 Station Road, Solihull, Birmingham, B91 3RT
Public Enquiry Office - Croydon
0870 606 7766
Lunar House, 40 Wellesley Road, Croydon, CR9 2BY
Public Enquiry Office - Glasgow
0870 606 7766
Festival Court, 200 Brand Street, Govan, Glasgow, G51 1DH
Public Enquiry Office - Liverpool
0870 606 7766
Reliance House, 20 Water Street, Liverpool, L2 8XU
Public Enquiry Office - Sheffield
0870 606 7766
Vulcan House, Orchard entrance, 6 Millsands, Sheffield S3 8NU