Do you hold a railcard?
You can currently get cheap advances from Chester, as stated above, but these tend to sell out very quickly. You may also consider splitting tickets at Crewe, for a time penalty of approx 45 mins. This would consist of a day return at £12 and a super off peak London Midland Only return at £29/Off peak return at £39, both of which require you to travel outside of the peaks but are not restricted to a specific train. Alternatively, London Midland advances are available for roughly £10 each way from Crewe.
Are you making any other journeys around London? If so, the £41 Crewe-London London Midland only day travelcard (includes unlimited travel in zones 1-6) may be worth purchasing.
Alternatively, advance tickets start at £15 from Liverpool/Crewe on Virgin Trains but tend to reach the £25+ mark very quickly so you'd have to be quick.
If you don't mind travelling via Birmingham, you could also consider splitting tickets there. Advances start at £7 for Chester-Brum and £6 for Brum-London.