The cheapest way involves the
X5 coach between Milton Keynes and Cambridge.
If you wish to take this option the X5 stops outside the station at Milton Keynes, and about a 20minute walk in Cambridge, of which directions for you are
here.
Tickets :
Off Peak Return £12.15 Coventry - Milton Keynes Central : Any Permitted (Fare is set by Virgin Trains, so you can use any VT service before 0930, this assuming you have a 16-25 railcard).
Bus Period Return £7.60 Milton Keynes Central - Cambridge Bus MK : Any Permitted (You can't buy this ticket online, you could purchase at Coventry station, on the date of travel. If they require a code tell them it's 1378 - J512.
Off Peak Return (
CZ) £12.00 Cambridge - Ipswich : Any Permitted
Total cost : £31.75
Example times for this Wednesday leaving at 0851 :
0851 Coventry - Milton Keynes Central 0918
0955 Milton Keynes Central Bay 35 - Cambridge Parkside 1200
1243 Cambridge Station - Ipswich 1400
Example times returning this Thursday around 1400
1419 Ipswich - Cambridge 1539
1630 Cambridge Parkside - Milton Keynes Central Bay 35 1830
1913 Milton Keynes Central - Coventry 1942
This option I have provided is more or less the same time as if you went on the train via Leicester & Peterborough.
Hope this helps.