You can go via Birmingham, Nuneaton, Nottingham, or even Doncaster & Stevenage (the latter most likely not on any single ticket).
You could try:
Liverpool - Nuneaton 17:47 arr Stafford 18:42
Stafford - Nuneaton 18:55 arr 19:35 £12 Advance
Nuneaton - Melton Mowbray 19:52 £9.50 Advance
Melton Mowbray - Cambridge 20:35 (same train) £11.30 advance
Hence £32.80 outbound
Or £9.50 on London Midland to Birmingham 17:04 arr. 18:48 and then onto the same XC train via Nuneaton & Melton Mowbray. BHM - Melton Mowbray is £10
So this route works out £2 cheaper (£30.80), but it starts 43 minutes earlier for the same arrival time.
On the 9th, Ely - Pbo is replaced by a bus. So going via London likely to be the best option. CBG - BHM is £14 Advance via Kings Cross and Euston on Virgin. Earliest arrival time 17:25.
£13 on the 17:39 London Midland train from Birmingham arriving Liverpool at 19:14.
So £27 for the return leg.
Or, if you must, the 14:00 to Ely, then the bus, arr 15:43, at £7.70 advance, then the 16:24 from Pbo to Liverpool arriving at 20:30, priced at £18.90 advance
Either way around £58, which is £27 cheaper than the off-peak return 'not via London'.