Petrina
You must be one very big Liverpool fan! Same like my mum. In fact she wants me to take her to Liverpool the next time she visits me in the UK.
I would generally consider late sept/oct to be off-peak season as things start to slow down by then.
London is one of the most expensive cities to live in England so I should think you would find accomodation in Liverpool to be relatively cheaper than in London. But if your main intention is to watch a Liverpool match than it might be better to just stay in the vicinity of Liverpool. Liverpool is also the home town of The Beatles so there are places of interest to visit.
I don't think it is very feasible to make day visits between London and Liverpool as they are quite far away from each other. You'll be spending a lot of time travelling and will only tire yourself out. Not really worth it in my opinion as you could spend that time visiting some really nice places in Britain.
A train will take about two and half hours while a bus is about five hours (could be longer if you have to change).
Why not plan your journey such that you spend a few days in London and its surrounding areas and then go Northwest to Liverpool. Spend a few days in Liverpool where you can consider a visit to Manchester or even the Lake District. Tbh I think the Lake District would make a more ideal place for a honeymoon than London. But if this is your first visit to Britain then I guess London is a must!
Another alternative is to fly to Manchester (you can also make Manchester your base as Manchester is pretty close to Liverpool). Stay a few days in the Northwest and then make your way down to London.
Anyway here are some webbies to help you along:
http://www.visitenglandsnorthwest.com/
http://www.visitbritain.co.uk/