I planned on getting a late, off peak ticket. I figured on trying to set it up where I can fly in and land early in London. Around 10am. Spend the day in London checking out the Military Museum, grab a late lunch and then get up to Liverpool on one of the post rush hour trains. But of course well thought out vacation plans usually get fu**ed up about 20 min after you land, so who knows. I pray to god that my trip doesn't coincide with Trumps London visit. If it does Ill just say I'm a Canadian.
If on a budget and you don't mind the longer travel, consider National Express or Megabus coaches. I've done the Liverpool - London route a few times when saving money and it can be ridiculously cheap, like 5 pounds. It takes about 6 hours, so that's not for everyone, of course. But I think the coaches are fairly comfortable and you could travel over the night if you want.